To solve for \( y \) in the equation
\[ \frac{y - 1}{4} + \frac{1}{3} = \frac{7}{12}, \]
we'll start by eliminating the fractions. The least common multiple (LCM) of the denominators 4, 3, and 12 is 12. We'll multiply each term by 12:
\[ 12 \left(\frac{y - 1}{4}\right) + 12 \left(\frac{1}{3}\right) = 12 \left(\frac{7}{12}\right). \]
This simplifies to:
\[ 3(y - 1) + 4 = 7. \]
Now, distribute the 3:
\[ 3y - 3 + 4 = 7. \]
Combining like terms gives:
\[ 3y + 1 = 7. \]
Next, isolate \( 3y \) by subtracting 1 from both sides:
\[ 3y = 7 - 1, \]
which simplifies to:
\[ 3y = 6. \]
Now divide both sides by 3:
\[ y = \frac{6}{3} = 2. \]
Thus, the solution is
\[ \boxed{2}. \]
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