5/8y - 1/2y + 1/12y = 1/4

To solve the equation \( \frac{5}{8}y - \frac{1}{2}y + \frac{1}{12}y = \frac{1}{4} \), let's first find a common denominator for the fractions involving \( y \).

The denominators are 8, 2, and 12. The least common multiple (LCM) of these numbers is 24.

Now, we can rewrite each term:

1. \( \frac{5}{8}y = \frac{5 \cdot 3}{8 \cdot 3}y = \frac{15}{24}y \)
2. \( \frac{1}{2}y = \frac{1 \cdot 12}{2 \cdot 12}y = \frac{12}{24}y \)
3. \( \frac{1}{12}y = \frac{1 \cdot 2}{12 \cdot 2}y = \frac{2}{24}y \)

Now, substitute these back into the equation:

\[ \frac{15}{24}y - \frac{12}{24}y + \frac{2}{24}y = \frac{1}{4} \]

Combining the fractions on the left side:

\[ \left( \frac{15 - 12 + 2}{24} \right)y = \frac{1}{4} \]

Simplifying the left side:

\[ \frac{5}{24}y = \frac{1}{4} \]

To isolate \( y \), multiply both sides by the reciprocal of \( \frac{5}{24} \), which is \( \frac{24}{5} \):

\[ y = \frac{1}{4} \cdot \frac{24}{5} \]

Calculating the right side:

\[ y = \frac{24}{20} = \frac{6}{5} \]

So, the solution is:

\[ \boxed{\frac{6}{5}} \]