2024 AMC 10B Problem 20

Three different pairs of shoes are placed in a row so that no left shoe is next to a right shoe from a different pair. In how many ways can these six shoes be lined up?

\textbf{(A)} 60 \qquad \textbf{(B)} 72 \qquad \textbf{(C)} 90 \qquad \textbf{(D)} 108 \qquad \textbf{(E)} 120

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