The angle 12x-6 is a vertical angle to the 90 degree angle (marked by the square red marker)
Vertical angles are congruent, aka equal, so that means 12x-6 is equal to 90
12x - 6 = 90
12x - 6 + 6 = 90 + 6 ... add 6 to both sides
12x = 96
12x/12 = 96/12 ... divide both sides by 12
x = 8
So the final answer is x = 8
Let's check the answer. We do this by plugging in x = 8 into the original equation
12x - 6 = 90
12*x - 6 = 90
12*8 - 6 = 90 ... replace x with 8
96 - 6 = 90
90 = 90
Since we get a true result (same number on both sides), this confirms we have the correct answer.