It is clear that $6$, $5$, and $4$ will not come together to get a [sum](https://artofproblemsolving.com/wiki/index.php/Sum) of $15$.
The faces $6$, $5$, and $3$ come together at a common vertex, making the [maximal](https://artofproblemsolving.com/wiki/index.php/Maximum) sum $6+5+3=14\rightarrow \boxed{\text{D}}$.
The figure may be folded along the lines shown to form a number cube.  Three number faces come together at each corner of the cube.  What is the largest sum of three numbers whose faces come together at a corner?

$\text{(A)}\ 11 \qquad \text{(B)}\ 12 \qquad \text{(C)}\ 13 \qquad \text{(D)}\ 14 \qquad \text{(E)}\ 15$