To solve for \( y \) in the given system of equations, we start with the two equations:
- \( x + 6y = 10 \) (Equation 1)
- \( -x + 3y = -15 \) (Equation 2)
We can add these two equations together to eliminate \( x \):
\[ (x + 6y) + (-x + 3y) = 10 + (-15) \]
This simplifies to:
\[ (0) + (6y + 3y) = -5 \]
Which further simplifies to:
\[ 9y = -5 \]
Now, we can solve for \( y \):
\[ y = -\frac{5}{9} \]
Thus, the value of \( y \) is:
\[ \boxed{-\frac{5}{9}} \]