To solve this equation, we first need to simplify the left side:

4 3/4 - (x - 2 5/8)

Convert 4 3/4 to an improper fraction:
4 3/4 = 19/4

Convert 2 5/8 to an improper fraction:
2 5/8 = 21/8

Now, rewrite the equation with the common denominator:
19/4 - (x - 21/8) = 3 5/6

Simplify the equation:
19/4 - x + 21/8 = 3 5/6
19/4 - x + 21/8 = 19/3

Now, convert 3 5/6 to an improper fraction:
3 5/6 = 19/6

Substitute back into the equation:
19/4 - x + 21/8 = 19/6

Next, combine the fractions:
38/8 - x + 21/8 = 19/6
59/8 - x = 19/6

To isolate x, we need to get rid of the fraction. We can do this by finding a common denominator between 8 and 6, which is 24:
(3/3)(59/8) - 3(3/3)(19/6) = (8/8)(19/6)
177/24 - 57/24 = 152/24
120/24 = 152/24
x = 120/24
x = 5

Therefore, the solution to the equation is x = 5.