Step 1 :
Factor out common factor $ \color{blue}{ y } $:
$$ 6x^2y+7xy^2+y^3 = y ( 6x^2+7xy+y^2 ) $$Step 2 :
$ 6x^2+7xy+y^2 $ can be written as
$$ 6x^2+7xy+y^2 = \left( 6x+y \right) \left( x+y \right)$$The explanation for this step cannot be generated.