Hi Sheileah,
Welcome to Yamaha Synth! Look no farther, you've found the place on the web for all things Yamaha concerning synthesizers!

Okay, first we have to tell you that you do not need the UR44 to record MIDI and Audio from the MOXF to your computer.
The MOXF has a built-in 4-in/2-out audio interface, plus it communicates on 5 Ports of MIDI with your computer via a single USB connection.

This does not mean you can't use the UR44, as you have it connected, it just means that you do not have to. The MOXF already has the functionality to record and playback both MIDI and Audio with your computer all by itself... Through a single USB cable connection.

What else are you going to connect to your computer in your setup?
You need to decide how you wish configure your setup...

Here are some things to consider:
When you connect the MOXF to your computer and use it as your MIDI/Audio interface you can use 4 Channels (2 Stereo pairs) of audio - USB 1/2 are used for the MOXF's A/D INPUT jacks (anything you connect to the back panel inputs will be routed as audio to your computer on the first pair of audio outputs, USB 1/2) - the A/D input is a single input and can be used for a microphone, or a guitar, or another keyboard, etc, etc.;
Your internal MOXF synth Parts are initially assigned to USB 3/4, but you have the option of assigning each Part, in turn, to the other pair, USB 1/2, when you wish to record a Part in isolation.

Now, you may have a reason for having purchased the UR44, it does allow you to connect microphones that require +48Volt Phantom Power. And it does have those killer Yamaha mic preamps. But if you use this as your audio interface, you must configure your setup to accommodate it. Before we give the information about how to configure your system, it would be extremely helpful if you provide us with an idea of how YOU would like to work... What you envision is going to be your workflow. What else (microphones, other keyboards, etc.) you wish to connect.

Since you are using a Macintosh computer you do have the option of connecting both devices as audio interfaces. But only one of them can be connected to your speakers. So monitoring requires you connect audio between devices. (But this will depend on your workflow... The order in which you approach your project.)

You have options... Cubase allows you to quickly reconfigure your system (it may seem now that this would be difficult, but once you see how it works, it is not difficult at all) the readon we mention this because everybody's workflow is a little different... You might create your music tracks first using the MOXF, Then reconfigure your setup for overdubbing vocals, guitars, etc. as an example. Do not assume that there is ONLY ONE configuration. Just FYI.

SETUP USING YOUR CURRENT CONFIGURATION
Let's get you up and running with your current configuration, using the information you have provided thus far. That is, using the Steinberg UR44 as your audio interface.
In Cubase
Go to DEVICES > DEVICE SETUP > VST AUDIO SYSTEM > select the UR44 as your ASIO DEVICE

Go to DEVICES > VST CONNECTIONS > select the INPUTS tab
If one does not exist create a Stereo bus (click ADD BUS > STEREO)
Set AUDIO DEVICE = UR44
Set the left and right DEVICE PORTS = UR44 port 3 and 4, respectively.

This stereo Input can now be used when you want record audio from your MOXF
Go to the main Cubase window
Go to PROJECT > ADD TRACK > AUDIO > create a stereo Audio Track
When it appears set its input to the Stereo Input you just created.

You do not mention how you have the MOXF connected to your computer for MIDI communication... So we will await that information. You can either connect the MOXF to your computer via USB, or via two standard MIDI cables through the UR44's 5-pin IN/OUT. Things to consider about MIDI... If you wish to use the MOXF EDITOR VST you will need to connect the MOXF directly to the computer via USB (again this is your choice).

As mentioned in this configuration the MOXF is just a single stereo device... Connected via the UR44's 3rd and 4th ports.

Let us know.