Answer
$-12$
Work Step by Step
If $A$ and $B$ are $n\times n$ matrices, then $det(AB)=det(A)det(B)$. Also $det(A^T)=det(A)$.
Hence here $det(A^TB)=det(A^T)det(B)=det(A)det(B)=3(-4)=-12$.
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