Let's start with the equation you provided:
\[ h - 3 = 9h + 9 \]
Now, we want to subtract 9 from both sides of the equation:
\[ h - 3 - 9 = 9h + 9 - 9 \]
This simplifies to:
\[ h - 12 = 9h \]
Next, we want to isolate \(h\) on the left side. To do that, we can subtract \(h\) from both sides:
\[ h - h - 12 = 9h - h \]
This simplifies to:
\[ -12 = 8h \]
Now, if you want to express this in terms of \(h\), you can divide both sides by 8:
\[ h = -\frac{12}{8} \]
This further simplifies to:
\[ h = -\frac{3}{2} \quad \text{or} \quad h = -1.5 \]
So the final answer is \(h = -\frac{3}{2}\).