Expand the options and collect like terms to check which gives the presented expression.

Expansion of Options A:

(x+y+6)(x+y-3) → \(x^2+xy-3x + xy+y^2-3y +6x+6y-18\) 

Collect like terms: \(x^2 + xy + xy + y^2 +6x - 3x +6y - 3y - 18\)

= \(x^2 + 2xy + y^2 + 3x + 3y - 18\)