`a)`

`(2x+3y)^2 - (2x-3y)^2`

`=4x^2 +12xy +9y^2 - 4x^2 +12xy-9y^2`

`=24xy`

`b)`

`(2x+1)^2 -2(2x-1)(1+2x)+4x^2 -4x+1`

`=4x^2 +4x+1-2(4x^2 -1)+4x^2 -4x+1`

`=8x^2 +2 -8x^2 +2`

`=4`

`c)`

`(x-y)^2 + (x+y)^2 + 2(x^2 -y^2) -4x^2`

`=x^2 -2xy+y^2 +x^2 +2xy+y^2 +2x^2 -2y^2 -4x^2`

`=0`

`d)`

`(3x+y)^2 - 6(3x+y)(x+2y)+9(x+2y)^2`

`=9x^2 +6xy+y^2 -6(3x^2 +7xy+2y^2) + 9(x^2 +4xy+4y^2)`

`=9x^2 +6xy+y^2 + (-18x^2 -42xy-12y^2) + (9x^2 +36xy+36y^2)`

`=25y^2`

`e)`

`12(x+2)-8+(x+2)^3 -6(x+2)^2`

`=12x+24x-8+x^3 +6x^2 +12x+8-6(x^2 +4x+4)`

`=x^3 +6x^2 +48x-6x^2 -24x-24`

`=x^3 +24x-24`

`f)`

`(3x+2y)(9x^2 -6xy+4y^2) - (2y-3x)(4y^2 +6xy+9x^2)`

`=27x^3 +8y^3 -8y^3 +27x^3`

`=54x^3`.