We are given that,

We need to find the value of x.

Determinant of 2 × 2 matrix is found as,

Let us take left hand side (LHS) of the given matrix equation.

⇒ LHS = 3x × 4 – 7 × (-2)

⇒ LHS = 12x – (-14)

⇒ LHS = 12x + 14

Let us take right hand side (RHS) of the given matrix equation.

⇒ RHS = 8 × 4 – 7 × 6

⇒ RHS = 32 – 42

⇒ RHS = -10

Now,

LHS = RHS

⇒ 12x + 14 = -10

⇒ 12x = -10 – 14

⇒ 12x = -24

⇒ x = -2

Thus, the value of x is -2.