Let's solve the equation step by step:
The equation is:
\[ -4y + 10 = -2(3y + 4) \]
First, distribute \(-2\) on the right side:
\[ -4y + 10 = -2 \cdot 3y - 2 \cdot 4 \] \[ -4y + 10 = -6y - 8 \]
Next, we want to isolate \(y\). We'll first move all terms involving \(y\) to one side and constant terms to the other side. Let's add \(6y\) to both sides:
\[ -4y + 6y + 10 = -8 \] \[ 2y + 10 = -8 \]
Now, subtract \(10\) from both sides:
\[ 2y = -8 - 10 \] \[ 2y = -18 \]
Next, divide both sides by \(2\):
\[ y = \frac{-18}{2} \] \[ y = -9 \]
The solution is:
\[ y = -9 \]