You have 24 feet of the fence to make a rectanglar garden. Each side will measure a whole number of the feet. How many different-sized rectangular gardens can you make?
We can let the length of the rectangle be $x$ feet and the width be $y$ feet. Since both $x$ and $y$ are whole numbers, we need to find all possible pairs $(x,y)$ such that $x+y=12$. We can make a list of all possible pairs: \begin{align*}
(1,11) \\
(2,10) \\
(3,9) \\
(4,8) \\
(5,7) \\
(6,6) \\
\end{align*} There are $\boxed{6}$ possible pairs.