y-4 3/4=12 3/8

To solve the equation \( y - 4 \frac{3}{4} = 12 \frac{3}{8} \), we first convert the mixed numbers into improper fractions.

1. Convert \( 4 \frac{3}{4} \): \[ 4 \frac{3}{4} = 4 \times 4 + 3 = 16 + 3 = 19/4 \]

2. Convert \( 12 \frac{3}{8} \): \[ 12 \frac{3}{8} = 12 \times 8 + 3 = 96 + 3 = 99/8 \]

Now, substitute these values back into the equation:

\[ y - \frac{19}{4} = \frac{99}{8} \]

Next, to isolate \( y \), add \(\frac{19}{4}\) to both sides. We will need a common denominator to add the fractions. The common denominator of 4 and 8 is 8.

Convert \(\frac{19}{4}\) into eighths: \[ \frac{19}{4} = \frac{19 \times 2}{4 \times 2} = \frac{38}{8} \]

Now we can rewrite the equation: \[ y - \frac{38}{8} = \frac{99}{8} \]

Add \(\frac{38}{8}\) to both sides: \[ y = \frac{99}{8} + \frac{38}{8} = \frac{99 + 38}{8} = \frac{137}{8} \]

Thus, the solution is: \[ y = \frac{137}{8} \]

If you want to convert this back to a mixed number: \[ \frac{137}{8} = 17 \frac{1}{8} \]

So, the final answer is: \[ y = 17 \frac{1}{8} \]