To find the length \( L \) of the pendulum given the period \( T = 6.28 \) seconds, we can start from the formula:
\[ T = 2\pi \sqrt{\frac{L}{32}} \]
We can substitute \( \pi \) with \( 3.14 \):
\[ T = 2 \times 3.14 \sqrt{\frac{L}{32}} \]
Now we can set this equal to the given period:
\[ 6.28 = 2 \times 3.14 \sqrt{\frac{L}{32}} \]
Calculating \( 2 \times 3.14 \):
\[ 2 \times 3.14 = 6.28 \]
Now we have:
\[ 6.28 = 6.28 \sqrt{\frac{L}{32}} \]
To isolate \( \sqrt{\frac{L}{32}} \), we can divide both sides by \( 6.28 \):
\[ 1 = \sqrt{\frac{L}{32}} \]
Now, squaring both sides gives:
\[ 1^2 = \left(\sqrt{\frac{L}{32}}\right)^2 \]
This simplifies to:
\[ 1 = \frac{L}{32} \]
To solve for \( L \), we multiply both sides by \( 32 \):
\[ L = 32 \]
Therefore, the length \( L \) of the pendulum is:
\[ \boxed{32 \text{ feet}} \]