Given :
[tex](-12z^2+8z-15)-(4z^2+13)[/tex]Take the minus sign inside the bracket.
[tex]=-12z^2+8z-15-4z^2-13[/tex]Solve like terms, like terms are terms that contain the same variables with the same power.
[tex]=-12z^2-4z^2+8z-15-13[/tex][tex]=-16z^2+8z-28[/tex]Hence the answer is
[tex](-12z^2+8z-15)-(4z^2+13)=-16z^2+8z-28[/tex]