To subtract \( h \) from both sides of the equation \( h - 3 = 9h + 9 \):
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Start with the original equation:
\[ h - 3 = 9h + 9 \]
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Subtract \( h \) from both sides:
\[ h - h - 3 = 9h - h + 9 \]
This simplifies to:
\[ -3 = 8h + 9 \]
So, after moving \( h \) from the left side to the right side, you get:
\[ -3 = 8h + 9 \]