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The given function is
[tex]\begin{gathered} x^2-3x-6 \\ \text{gog(x)}=(x^2-3x-6)^2-3(x^2-3x-6)-6 \\ \text{Here to get gog(x), the fuunction g(x) is writtenin place of x variable in g(x) function} \end{gathered}[/tex]Substitute x=-2 in the function gog(x)
[tex]\begin{gathered} \text{gog(-2)}=((-2)^2-3\ast-2-6)^2-3((-2)^2-3\ast-2-6)-6 \\ =(4+6-6)^2-3(4+6-6)-6 \\ =4^2-3\ast4-6 \\ =16-12-6 \\ =-2 \end{gathered}[/tex]Therefore, the value of gog(-2) is -2