We are asked to solve the equation $\frac{y}{4} - \frac{2y}{3} = 16$ for $y$.

1. Problem Description

We are asked to solve the equation $\frac{y}{4} - \frac{2y}{3} = 16$ for $y$.

2. Solution Steps

First, find a common denominator for the fractions. The least common multiple of 4 and 3 is

1

2. Multiply both sides of the equation by 12:

$12(\frac{y}{4} - \frac{2y}{3}) = 12(16)$

Distribute the 12 on the left side:

$12 \cdot \frac{y}{4} - 12 \cdot \frac{2y}{3} = 192$

Simplify the fractions:

$3y - 4(2y) = 192$

$3y - 8y = 192$

Combine like terms:

$-5y = 192$

Divide both sides by -5 to solve for $y$:

$y = \frac{192}{-5}$

$y = -\frac{192}{5}$

3. Final Answer

$y = -\frac{192}{5}$