Answer
$2(3x+4)(9x+13) .$
Work Step by Step
We factor out $3x+4$ and then distribute, combine like terms and simplify as follows:\begin{align*} 2(3x + 4)^2 & + (2x + 3) \cdot 2(3x + 4) \cdot 3\\ &=(3x+4)[2(3x+4)+2\cdot 3(2x+3)]\\ &=(3x+4)(6x+8+12x+18)\\ &=(3x+4)(18x+26)\\ &=2(3x+4)(9x+13) . \end{align*}