Does the same determinant make two matrices equal to each other?

That style of brackets usually refers to the matrix itself, rather than the determinant. The question either uses an unusual style, or is in error.

If the problem is about an equality of the determinant, all you have to do is compute the determinants separately. The determinant of the $3\times 3$ matrix is $$ (2)(0)(6) + (-1)(5)(4) + (4)(3)(1) - (4)(0)(4) - (1)(5)(2) - (6)(3)(-1) = 0 - 20 + 12 - 0 - 10 + 18 = 0. $$ The $2\times 2$ determinant is just $x^{2} - 20$. Then, we arrive at the equation $$ 0 = x^{2} - 20 $$ which has two possible solutions: $x=\sqrt{20}$ or $x=-\sqrt{20}$. Thus, the answer is (D) if the question refers to determinants.

If not, then there is no solution.