To solve this equation, we need to simplify each side first.

Starting with the left side:

3/8(12x-16)-x/2
= 3/8 12x - 3/8 16 - x/2
= 36/8x - 48/8 - x/2
= 9/2x - 6 - x/2

Now, simplifying the right side:

51/4 - 5/4(4-x)
= 51/4 - 5/4 * 4 + 5/4x
= 51/4 - 20/4 + 5/4x
= 31/4 + 5/4x

Therefore, the equation becomes:

9/2x - 6 - x/2 = 31/4 + 5/4x

Next, we need to combine like terms:

9/2x - x/2 - 5/4x = 31/4 + 6
(9/2 - 1/2 - 5/4)x = 31/4 + 24/4
(18/4 - 4/4 - 5/4)x = 55/4
(9/4)x = 55/4

Now, we can solve for x:

x = (55/4) / (9/4)
x = 55/4 * 4/9
x = 55/9

Therefore, the solution to the equation is x = 55/9.