The knobs (17) can assume many modes. If you press the button labeled as (15) on the same figure then the 4 knobs will assume non-assignable (user configurable) functions and instead will be one of 4 sets of fixed functions. Either TONE or EG/FX or EQ or ARP/MS. And when you press button (15) aka "Knob Function" button the [ASSIGN] button is turned off signaling the knobs are no longer user assignable and instead assume the personality of being one of the 4 sets of fixed values (TONE or EG/FX or EQ or ARP/MS). You press the Knob Function button while [ASSIGN] is not lit in order to cycle through the 4 functions (TONE then EG/FX then EQ then ARP/MS). For each of the "knob function" personalities - when the knobs are fixed-function - what each of the 4 knobs will be set to is labeled next to the fixed knob function categories. For tone, the 1st knob adjusts "cutoff" and knob 2 adjusts "resonance" and knob 3 adjusts "pan" and knob 4 adjusts "portamento". You can look at the rest of the labels on your MODX above the knobs to see what other categories (EG/FX or EQ or ARP/MS) will set the 4 knobs to.

That's the context of the 4 knobs when [ASSIGN] is NOT lit. But it helps to differentiate what is happening when [ASSIGN] is lit.

When you press the [ASSIGN] button, the 4 knobs assume the user-configurable assignable values. There are actually two different sets of assignable values. Just like "knob function" had 4 categories - and shows which category is active by 4 corresponding LEDs - the [ASSIGN] mode has a couple categories so [ASSIGN] can set the 4 knobs to one of two different modes. [ASSIGN] can either mean PART assignable knobs or COMMON assignable knobs. The documentation calls this "Performance Control Status" (I called it COMMON category) or "Part Control Status" (I called this PART category).

Page 30 of the MODX owner's manual ( https://usa.yamaha.com/files/download/other_assets/5/1162395/modx6_modx7_modx8_en_om_a0.pdf ) describes all of this.

One way to force COMMON ("Performance Control Status" ) mode is to press the [PERFORMANCE] (HOME) button aka button (35) in the owner's manual figure on the next page. The owner's manual page 30 also describes how to use the touchscreen to force COMMON mode under the heading "For controlling the entire Performance". And if the [ASSIGN] button is lit, then this means the 4 knobs will be Performance COMMON assignable knobs.

Move the cursor to the desired Performance name from the Performance Play display. Or turn the [PART SELECT MUTE/
SOLO] button and select “Common” to enable the Performance Control status, and operate Knobs 1–4 (5–8).

... and the following heading "For controlling the desired Part" describes how to force PART mode. And if you follow this while the [ASSIGN] button is lit then the 4 knobs will be PART assignable knobs.

Move the cursor to the desired Part name from the Performance Play display. Or turn the [PART SELECT MUTE/SOLO]
button and select any of the “1” to “16” buttons to enable the Part Control status, and operate Knobs 1–4 (5–8).

... and finally - to the "meat" after description of the side dishes. At least now we have some terms defined.

If [ASSIGN] is lit and the current mode is "Performance Control Status" (aka COMMON) then the knobs will be configured as seen in the "Edit - Common/Audio" section with menu "Control" -> "Control Assign". This is shown in the MODX reference manual page 166 ( https://usa.yamaha.com/files/download/other_assets/2/1192582/modx_en_rm_a0.pdf ). To get to this menu, you can use either method:

[PERFORMANCE (HOME)] -> [EDIT] -> [Control] -> [Control Assign]
or
Touch [Edit Super Knob] in the Super Knob display

Then if you touch "Display Filter" and set to "AsgnKnob 1-8" - then this should show assignments of the COMMON level assignable knobs. Since, on this same screen, you can set the destination parameter for each assignable knob (COMMON) and change the curve type - this is what allows the user to configure what each knob is doing. And this is why they when you have this kind of configuration for each knob the knobs are labeled as "ASSIGN" (assignable).

If [ASSIGN] is lit and the current mode is "Part Control Status" (aka PART) then the knobs will be configured as seen in the "Edit - Part# - Common" section (where # is 1-16) with menu "Mod/Control" -> "Control Assign". This is shown in the MODX reference manual page 100. To get to this menu, the document states you press:

[PERFORMANCE (HOME)] -> [EDIT] -> Part selection -> Element [Common] -> [Mod/Control] -> [Control Assign]

Set the "Display Filter" to AsgnKnob 1-8 to show the PART assignable knob settings. Since, on this same screen, you can set the destination parameter for each assignable knob (PART) and change the curve type - this is what allows the user to configure what each knob is doing. And this is why they when you have this kind of configuration for each knob the knobs are labeled as "ASSIGN" (assignable).

What "parameters of sound" each knob is offsetting while [ASSIGN] is lit depends on these above configuration menus and how the assignable knob number has been associated with a destination. The source -> destination relationship is configured on these screens mentioned above. And the destinations available are numerous for PART level (at least 100 options). At the COMMON level - each COMMON assignable knob is a bit more limited in that its destination will be any of the PARTs' assignable knob and not directly a parameter. This is a means for superknob to affect PART level destinations because superknob only directly controls COMMON assignable knobs - then each COMMON assignable knob can be configured in the menu mentioned above "Edit - Common/Audio" section to a destination of one of the PART level knobs.

A side note - there are only 4 physical knobs - but there are actually 8 knobs available. You access each "bank" of assignable knobs by pressing the [ASSIGN] button. In other words, if the [ASSIGN] button is currently lit - then you press the [ASSIGN] button again - the 4 knobs will toggle between representing knobs 1-4 (one bank of assignable knobs) to knobs 5-8 (the second bank of assignable knobs).