Convolution and impulse respon

I looked at the book and looked at so many examples. I am so confused at how to calculate convolution. I know how to do in graphical way, but I can not understand how to calculate in mathematical way. Below is the question and answer. I have trouble understand part b of the question.

I know x(n) convolution with h(n) is x(k) multiplies h(n-k)

I tried to do it this way:

I think they use k = 2, but I am not sure though.

h4(n) * h3(n-2)
= delta (n-2) multiplies (n-2+1)u(n-2)
= (n-1) delta(n-2)

But it is different than the answer they provide. I totally don't understand. So please give me step by step. I really want to understand this subject. thank you

圖片參考：http://imgcld.yimg.com/8/n/HA00799676/o/701110020020813873470460.jpg