Why are the two molecules identical? Every time I assign priority to the stereocenters I end up getting RS for the first one and SR for the second one. Where am I going wrong?

You seem to have several versions of the molecule in different pics!

 

So far as I can tell it is a six carbon main chain with two methyl side groups emanating from C3 and C4.

In that case the molecule is symmetrical about the C3-C4 bond.

Here is a pic of a model of what I mean.

The main chain is shown in grey and the side methyls are blue and red.

 

Sorry I should've labeled the pictures better, the first pic was the original problem the rest was the work I'd done. I got it now though, thanks!

Both are same. 2nd one is another way of writing the same molecule. Hint: when you exchange to bonds with each other, the configuration is inverted i.e. from R to S or S to R.