AMC 10 2014a

Roy's cat eats $\frac{1}{3}$ of a can of cat food every morning and $\frac{1}{4}$ of a can of cat food every evening. Before feeding his cat on Monday morning, Roy opened a box containing $6$ cans of cat food. On what day of the week did the cat finish eating all the cat food in the box? ${ \textbf{(A)}\ \text{Tuesday} \textbf{(B)}\ \text{Wednesday} \textbf{(C)}\ \text{Thursday} \textbf{(D)}}\ \text{Friday} \textbf{(E)}\ \text{Saturday}$