To factor $ 10ab+15b+4a+6 $ we can use factoring by grouping.
Group $ \color{blue}{ 10ab }$ with $ \color{blue}{ 15b }$ and $ \color{red}{ 4a }$ with $ \color{red}{ 6 }$ then factor each group.
$$ \begin{aligned} 10ab+15b+4a+6 &= ( \color{blue}{ 10ab+15b } ) + ( \color{red}{ 4a+6 }) = \\ &= \color{blue}{ 5b( 2a+3 )} + \color{red}{ 2( 2a+3 ) } = \\ &= (5b+2)(2a+3) \end{aligned} $$