Let's simplify the expression step by step:

6(3x + 6) - 4(3x + 6)
= 18x + 36 - 12x - 24
= 18x - 12x + 36 - 24
= 6x + 12

Now, we have:

6x + 12 = 60

Subtract 12 from both sides:

6x = 48

Divide by 6 on both sides:

x = 8

Therefore, the value of x that satisfies the equation is x = 8.