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