To solve this equation, we need to simplify the expressions on both sides of the equation and then isolate the variable x.

Starting with the right side of the equation:
7/8 - 5/24 = (21/24) - (5/24) = 16/24 = 2/3

Now we substitute this back into the original equation:
x - 7/12 = 2/3

To isolate x, we add 7/12 to both sides:
x = 2/3 + 7/12
x = 8/12 + 7/12
x = 15/12
x = 5/4

Therefore, the solution to the equation X - 7/12 = 7/8 - 5/24 is x = 5/4.