So I had this question (f) at my last exam that I failed and I'm now studying for my re-exam, the problem is that I still don't know what the answer is supposed to be in this question (f):
Do you have any suggestions how to solve it?
The only thing you need to know is that any sequence convolved with a (shifted) delta impulse is a shifted version of itself:
Apply this to the expression $u[n]*(\delta[n]-\delta[n-1])$, and realize that what you're left with is a very simple sequence. (The result of (a) will be helpful.)
Then convolve this very simple sequence with $x[n]$ to get the final result.
x(n)*[d(n)-d(n-1)]=x(n)*d(n)-x(n)*d(n-1) = x(n)-x(n-1)