Answer
$0$
Work Step by Step
The determinant for a $2 \times 2$ matrix $\begin{bmatrix} a_{11} & a_{12} \\
a_{21} & a_{22} \\ \end{bmatrix}$ is defined as:
$$\begin{vmatrix} a_{11} & a_{12} \\
a_{21} & a_{22} \\ \end{vmatrix}=a_{11}a_{22}-a_{12}a_{21}$$
Thus, using the formula above gives:
\begin{align*}
\begin{vmatrix} x& 4x \\
\\2x & 8x \\ \end{vmatrix}&=(x)(8x) -(2x)(4x) \\&=8x^2-8x^2 \\\\&=0
\end{align*}
Therefore, the determinant is $0$.
