To factor $ 15xy+9x+20y+12 $ we can use factoring by grouping.
Group $ \color{blue}{ 15xy }$ with $ \color{blue}{ 9x }$ and $ \color{red}{ 20y }$ with $ \color{red}{ 12 }$ then factor each group.
$$ \begin{aligned} 15xy+9x+20y+12 &= ( \color{blue}{ 15xy+9x } ) + ( \color{red}{ 20y+12 }) = \\ &= \color{blue}{ 3x( 5y+3 )} + \color{red}{ 4( 5y+3 ) } = \\ &= (3x+4)(5y+3) \end{aligned} $$