1. **State the problem:** We need to find the expression that represents the perimeter of a triangle with side lengths labeled as $2b + 1$, $-4 + 3b$, and $b$. 2. **Recall the formula for the perimeter of a triangle:** $$\text{Perimeter} = \text{sum of all side lengths}$$ 3. **Add the side lengths:** $$ (2b + 1) + (-4 + 3b) + b $$ 4. **Combine like terms:** $$ 2b + 1 - 4 + 3b + b = (2b + 3b + b) + (1 - 4) $$ $$ = 6b - 3 $$ 5. **Final answer:** The expression representing the perimeter is $$\boxed{6b - 3}$$ This corresponds to option C.