2012 AMC 10A Problem 4

Let \angle ABC = 24^\circ and \angle ABD = 20^\circ. What is the smallest possible degree measure for angle CBD?

\textbf{(A)}\ 0\qquad\textbf{(B)}\ 2\qquad\textbf{(C)}\ 4\qquad\textbf{(D)}\ 6\qquad\textbf{(E)}\ 12

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