Would anyone be able to help out with the following discrete convolution question?
Hint

The simplest way is to use the Z transform property "convolution in time domain is multiplication in z domain".
See Z transform convolution

$$\mathrm{Z}(x[n]*h[n]) = \mathrm{Z}(x[n]) \times \mathrm{Z}(h[n])$$

Then you just need to do inverse Z transform.

Some typical Z transforms (including what is useful for you) can be found at Z transform pairs

Be careful with region of convergence (ROC).

It seems a homework?