Answer
We have:
\begin{align*}
\det(AB) &=\det(A)\det(B)\\ 24 &=24
\end{align*}
Work Step by Step
We calculate:
$$\det(AB)=\det\left( \begin{bmatrix} 3&0\\6&1 \end{bmatrix} \begin{bmatrix} 2&0\\5&4 \end{bmatrix} \right) = \det\left( \begin{bmatrix} 3\cdot2+0\cdot5&3\cdot0+0\cdot4\\6\cdot2+1\cdot5&6\cdot0+1\cdot4 \end{bmatrix} \right)=\\ \det\left( \begin{bmatrix} 6&0\\17&4 \end{bmatrix} \right) = 6\cdot4-17\cdot0=24$$
Then we calculate the other part:
$$\det(A)\det(B)\\ \det(A)=\left| \begin{matrix} 3&0\\6&1 \end{matrix}\right|=3\cdot1-6\cdot1=3\\ \det(B)=\left| \begin{matrix} 2&0\\5&4 \end{matrix}\right|=2\cdot4-5\cdot0=8\\ \det(A)\det(B)=3\cdot8=24$$
Therefor we have:
\begin{align*}
\det(AB) &=\det(A)\det(B)\\ 24 &=24
\end{align*}
