To solve for \( h \) in the equation
\[ 2(3h + 9) = 3(-2h + 10), \]
start by distributing the constants on both sides.
- Distributing on the left side:
\[ 2(3h) + 2(9) = 6h + 18. \]
- Distributing on the right side:
\[ 3(-2h) + 3(10) = -6h + 30. \]
Now rewrite the equation:
\[ 6h + 18 = -6h + 30. \]
Next, add \( 6h \) to both sides to combine like terms:
\[ 6h + 6h + 18 = 30, \]
which simplifies to:
\[ 12h + 18 = 30. \]
Now, subtract \( 18 \) from both sides:
\[ 12h = 30 - 18, \]
which simplifies to:
\[ 12h = 12. \]
Finally, divide both sides by \( 12 \):
\[ h = 1. \]
Thus, the solution is
\[ \boxed{1}. \]