2024 AMC 8 Problem 13

Buzz Bunny is hopping up and down a set of stairs, one step at a time. In how many ways can Buzz start on the ground, make a sequence of 6 hops, and end up back on the ground? (For example, one sequence of hops is up-up-down-down-up-down.)

\textbf{(A)} 4 \qquad \textbf{(B)} 5 \qquad \textbf{(C)} 6 \qquad \textbf{(D)} 8 \qquad \textbf{(E)} 12

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.