Factorise \( 2(2 x+y)-\left(6 x^{2}-3 x y\right] \)

Let's start by simplifying the expression you provided: \[ 2(2x + y) - (6x^2 - 3xy) \] First, distribute the 2 in the first term: \[ 4x + 2y - 6x^2 + 3xy \] Now, rearranging the terms gives: \[ -6x^2 + 3xy + 4x + 2y \] Next, we can group the terms for factoring: \[ -6x^2 + 3xy + 4x + 2y = -3x(2x - y) + 2(2x + y) \] Now, we can factor by grouping: \[ -3x(2x - y) + 2(2x + y) = (2 - 3x)(2x + y) \] So, the factorized form of the expression is: \[ (2 - 3x)(2x + y) \]