Answer: x = 2 and x = 4
Step-by-step explanation
Draw a horizontal line through y = -4. Notice the horizontal line passes through the parabola at (2,-4) and (4,-4)
This means x = 2 and x = 4 are solutions to f(x) = -4 when f(x) = 2(x-3)^2-6
As a check, let's try out x = 2
f(x) = 2(x-3)^2-6
f(2) = 2(2-3)^2-6
f(2) = 2(-1)^2-6
f(2) = 2(1)-6
f(2) = 2-6
f(2) = -4
This confirms that x = 2 leads to f(x) = -4.
Similar steps will result when x = 4.