If $\left|\begin{array}{cc}3 x & 7 \\ 4 & x\end{array}\right|=\left|\begin{array}{cc}6 & -2 \\ 4 & 2\end{array}\right|$, then the value of $x$ is :

$\pm 4$

$
\left|\begin{array}{cc}
3 x & 7 \\
4 & x
\end{array}\right|=\left|\begin{array}{cc}
6 & -2 \\
4 & 2
\end{array}\right|$

Solving the matrix we get

$3 x^2-7 \times 4=6 \times 2-(-2)(4)$

$3 x^2-28=12+8$

$3 x^2-28=20$

$3 x^2=20+28$

$3 x^2= 48$

$x^2= 16$

$x \pm 4$