Step-by-step Solution:

\[ \text{Sequence: } 3,\ 6,\ 18,\ 72,\ \ ?\ ,\ 432 \] \[ \text{Pattern (multipliers): } \times 2,\ \times 3,\ \times 4,\ \times 3,\ \times 2 \] \[ 3 \times 2 = 6,\quad 6 \times 3 = 18,\quad 18 \times 4 = 72,\quad 72 \times 3 = \boxed{216},\quad 216 \times 2 = 432 \] \[ \boxed{216} \]