1. **State the problem:** We need to write an expression for the perimeter of a triangle with two sides labeled $4y$ and one side labeled $3y$. 2. **Identify the sides:** The triangle has three sides: $4y$, $4y$, and $3y$. 3. **Write the perimeter expression:** The perimeter $P$ is the sum of all sides, so $$P = 4y + 4y + 3y$$ 4. **Simplify the expression:** Combine like terms, $$P = (4 + 4 + 3)y = 11y$$ 5. **Final answer:** The simplified expression for the perimeter is $$P = 11y$$