`a)`

`1/2xy^2(6xy+3/2x^3y-1)`

`=1/2xy^2. 6xy+1/2xy^2. 3/2x^3y-1/2xy^2. 1`

`=3x^2y^3+3/4x^4y^3-1/2xy^2`

`b)`

`(2x-1/2y)(2x+1/2y)`

`=(2x)^2-(1/2y)^2`

`=4x^2-1/4y^2`

`c)`

`24x^5y^3z^6:6x^4y^2z^3`

`=(24:6).(x^5:x^4).(y^3:y^2).(z^6:z^3)`

`=4xyz^3`

`d)`

`(3x^6y^7z^6+2x^5y^3z^7-6x^5y^3z^8):42x^3y^3z^6`

`=3x^6y^7z^6:42x^3y^3z^6+2x^5y^3z^7:42x^3y^3z^6-6x^5y^3z^8:42x^3y^3z^6`

`=1/14x^3y^4+1/21x^2z-1/7x^2z^2`

`#owen`