To solve this equation, we need to combine like terms on the left side:

5/8b - 7/12b + 5/6b

To find a common denominator, we need to find the LCM of 8, 12, and 6 which is 24.

Now, rewrite each fraction with the denominator of 24:

(5/8) (3/3) = 15/24b
(7/12) (2/2) = 14/24b
(5/6) * (4/4) = 20/24b

So the equation becomes:

15/24b - 14/24b + 20/24b =1/4

Now combine the like terms:

15/24b - 14/24b + 20/24b =1/4
(15 - 14 + 20) / 24b = 1/4
21 / 24b = 1/4
21 / 24b = 6 / 24

Therefore, b = 6