Guys how can I move UV's?

I’m trying to make something like this:

But I cant figure out a way to move the pupils…

You can do this by performing some basic maths on the output from a texcoord node. Look into the divide and add nodes for moving and scaling the UVs around to the right part of the texture and possibly component mask to move the X and Y coordinates independently before using Append to re-combine them. Here’s a link to the documentation on material maths expressions

Once you have a basic setup in place, you can manipulate it at runtime via dynamic material instances and scalar parameters.