To factor $ 6xy+27x+2y+9 $ we can use factoring by grouping.
Group $ \color{blue}{ 6xy }$ with $ \color{blue}{ 27x }$ and $ \color{red}{ 2y }$ with $ \color{red}{ 9 }$ then factor each group.
$$ \begin{aligned} 6xy+27x+2y+9 &= ( \color{blue}{ 6xy+27x } ) + ( \color{red}{ 2y+9 }) = \\ &= \color{blue}{ 3x( 2y+9 )} + \color{red}{ 1( 2y+9 ) } = \\ &= (3x+1)(2y+9) \end{aligned} $$