Carmen simplifies the expression \( (4 y+8 x+6)+25+(4 x+6 y+7) \). The coefficient of the variable \( y \) in her simplified answer is 4 . 6. 10 . 12.

To simplify the expression \( (4y + 8x + 6) + 25 + (4x + 6y + 7) \), we first combine like terms. 1. Combine the constant terms: \( 6 + 25 + 7 = 38 \). 2. For the terms with \( x \): \( 8x + 4x = 12x \). 3. For the terms with \( y \): \( 4y + 6y = 10y \). So the simplified expression is \( 12x + 10y + 38 \). The coefficient of the variable \( y \) in her simplified answer is **10**.