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before the section of problems it says "write each product as a trinomial"

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When it says "write each product as a trinomial", this basically means that your final product will have three (tri) parts.

(8z + 7)(z-2)- To solve this method, you have to use the FOIL method- F-FIRST, O-OUTSIDE, I-INSIDE, L-LAST

First: 8z x z= 8z^2

Outside: 8z x -2= -16z

Inside: 7 x z= 7z

Last: 7 x -2= -14

After putting it all together, your final answer will be 8z^2 -11z-14


Good catch on a simple mistake!
-16z + 7z = -9z

So the answer should be: 8 z^2 - 9z  - 14