To solve this equation, we first need to simplify it by combining like terms.

12 - (x + 1 3/8) = 10 7/14

First, we convert the mixed number 1 3/8 to an improper fraction:

1 3/8 = (8 * 1 + 3) / 8 = 11/8

So the equation becomes:

12 - (x + 11/8) = 10 7/14

Next, simplify the equation further:

12 - x - 11/8 = 10 1/2

Combine like terms by subtracting the fractions:

12 - x - 11/8 = 21/2

12 - x - 1 3/8 = 21/2

Now simplify further by combining like terms:

10 7/8 - x = 21/2

To isolate x, we need to subtract 10 7/8 from both sides:

x = 10 7/8 - 21/2

x = 86/8 - 21/2

x = 43/4 - 42/8

x = (86 - 42) / 8

x = 44 / 8

x = 5 1/2

Therefore, the solution to the equation 12 - (x + 1 3/8) = 10 7/14 is x = 5 1/2.