Using FOIL you multiply each term in the first set of parentheses by each term in the other set, then combine all like terms:
(3z+3)(5z+8)
3z x 5z = 15z^2
3z x 8 = 24z
3 x 5z = 15z
3 x 8 = 24
So you now have:
15z^2 + 24z + 15z + 24
Simplify to:
15^2 + 39z + 24