To find the height of the hovercraft at the time of takeoff, we need to evaluate the height function \( h(x) \) at \( x = 0 \).
The height function is given by:
\[ h(x) = -3(x-3)^2 + 108 \]
Now, substitute \( x = 0 \):
\[ h(0) = -3(0-3)^2 + 108 \]
Calculate \( (0-3)^2 \):
\[ (0-3)^2 = (-3)^2 = 9 \]
Now substitute this value back into the equation:
\[ h(0) = -3 \cdot 9 + 108 \] \[ h(0) = -27 + 108 \] \[ h(0) = 81 \]
Therefore, the height of the hovercraft at the time of takeoff is \( \boxed{81} \) meters.