Y-7/12•y=4 1/6

To solve the equation \( y - \frac{7}{12} y = 4 \frac{1}{6} \), we can follow these steps:

1. Convert the mixed number \( 4 \frac{1}{6} \) into an improper fraction: \[ 4 \frac{1}{6} = 4 + \frac{1}{6} = \frac{24}{6} + \frac{1}{6} = \frac{25}{6} \]

2. Now rewrite the equation: \[ y - \frac{7}{12} y = \frac{25}{6} \]

3. Combine the terms on the left side. To do this, we can factor \( y \): \[ y(1 - \frac{7}{12}) = \frac{25}{6} \]

4. Calculate \( 1 - \frac{7}{12} \): \[ 1 = \frac{12}{12} \quad \text{so} \quad 1 - \frac{7}{12} = \frac{12}{12} - \frac{7}{12} = \frac{5}{12} \] The equation now looks like: \[ y \cdot \frac{5}{12} = \frac{25}{6} \]

5. To isolate \( y \), multiply both sides by the reciprocal of \( \frac{5}{12} \), which is \( \frac{12}{5} \): \[ y = \frac{25}{6} \cdot \frac{12}{5} \]

6. Multiply the fractions: \[ y = \frac{25 \cdot 12}{6 \cdot 5} = \frac{300}{30} = 10 \]

Thus, the solution is: \[ \boxed{10} \]