To solve the equation, we can take the square root of both sides:

√((x-2)^2) = √36

Simplifying, we have:

x - 2 = ±6

Now, we can solve for x by adding 2 to both sides:

x = 2 ± 6

This gives us two possible solutions:

x = 2 + 6 = 8

x = 2 - 6 = -4

Therefore, the solutions to the equation (x-2)^2 = 36 are x = 8 and x = -4.