To factor $ uv-9u+2v-18 $ we can use factoring by grouping.
Group $ \color{blue}{ uv }$ with $ \color{blue}{ -9u }$ and $ \color{red}{ 2v }$ with $ \color{red}{ -18 }$ then factor each group.
$$ \begin{aligned} uv-9u+2v-18 &= ( \color{blue}{ uv-9u } ) + ( \color{red}{ 2v-18 }) = \\ &= \color{blue}{ u( v-9 )} + \color{red}{ 2( v-9 ) } = \\ &= (u+2)(v-9) \end{aligned} $$