In my programming class, we need to write a program where the user is prompted for a value. Once that value is provided, the program is supposed to multiply its digits. For example: if the user typed 1234, it would multiply 1*2*3*4 and give the answer. I'm not sure how to multiply the digits and my teacher mentioned using a while loop.

This problem is really simple:
1. You can loop python strings like anyway other container.
2. You can convert a digit string ("1") to an integer (1) using int()

I'm not even going to tell you how to do the rest. Go ahead and prove that you aren't lazy.

I'm not sure how to multiply the digits

Here's multiplication in Python

>>> 1 * 2 * 3 * 4

I suggest you peruse the Python documentation to learn yourself something. I suggest the First Steps Towards Programming section