Let $\begin{vmatrix}x&2\\18&x\end{vmatrix}=\begin{vmatrix}-4&-2\\-8&-4\end{vmatrix}$. Then

(A) $x = -4$
(B) $x = -6$
(C) $x = 4$
(D) $x = 6$

Choose the correct answer from the options given below:

(B) and (D) only

The correct answer is Option (4) → (B) and (D) only

Given:

$\begin{vmatrix} x & 2 \\ 18 & x \end{vmatrix} = \begin{vmatrix} -4 & -2 \\ -8 & -4 \end{vmatrix}$

Evaluate both determinants.

Left side:

$x\cdot x - 18\cdot 2 = x^{2} - 36$

Right side:

$(-4)(-4) - (-8)(-2) = 16 - 16 = 0$

Hence:

$x^{2} - 36 = 0$

$x^{2} = 36$

$x = \pm 6$

From options, $x=-6$ and $x=6$ satisfy.

Final answer: $x=-6$ and $x=6$