[(-5 z^2-11 z-12) - (9 z^2-34 z+2)] - (-20 z^2+38 z-24)

need help to solve what do the brackets mean[]

the bracket means we have to solve first the quantity inside this grouping symbol. bracket is used not to overuse parenthesis (since parenthesis is already use.)
[(-5 z^2-11 z-12) - (9 z^2-34 z+2)] operate on this first, then the result in simplifying this will used together with the third given.

(-14z^2 + 23z -14) - (-20 z^2+38 z-24)

6z^2- 15z 10

6 z^2 - 15z +10

just distribute the "-" signs and expand and simplify