a) `3cd-6bd`
`= 3d.c-2b.3d`
`= 3d(c-2b)`
b) `4m^{2}n-8mn^{2}-12n^{2}`
`= 4n.m^{2}-4n.2mn-4n.3n`
`= 4n(m^{2}-2mn-3n)`
c) `4x^{3}y^{3}-8x^{2}y^{2}`
`= 4x^{2}y^{2}.xy-4x^{2}y^{2}.2`
`= 4x^{2}y^{2}(xy-2)`
d)`15x^{3}y^{2}+10x^{2}y^{2}-2x^{2}y^{3}` `=x^{2}y^{2}.15x+x^{2}y^{2}.10-x^{2}y^{2}.2y`
`= x^{2}y^{2}(15x+10-2y)`
e) `-4x^{3}y-6x^{2}y^{2}-8x^{4}y^{3}`
`=-2x^{2}y.2x-2x^{2}y.3y-2x^{2}y.4x^{2}y`
`= -2x^{2}y(2x+3y+4x^{2}y)`