a) $4x^2-6xy^2=2x.2x-2x.3y^2=2x(2x-3y^2)$
b) $3x(x-1)+2y(1-x)=3x(x-1)-2y(x-1)=(x-1)(3x-2y)$
c) $x(x-y)-3x+3y=x(x-y)-3(x-y)=(x-y)(x-3)$
d) $x^2-9y^2=x^2-(3y)^2=(x-3y)(x+3y)$
e) $x^2+4y^2+4xy=x^2+2.x.2y+(2y)^2=(x+2y)^2$
f) $9x^2-2=(3x)^2-(\sqrt 2)^2=(3x-\sqrt 2)(3x+\sqrt 2)$