We need

#(x^n)'=nx^(n-1)#

We calculate the derivative

#y=2x^3+3x^2-12x#

#dy/dx=6x^2+6x-12#

To find the critical points, let #dy/dx=0#

#6x^2+6x-12=6(x^2+x-2)=0#

#6(x-1)(x+2)=0#

Therefore, #x=1# and #x=-2#

We can make a variation table

#color(white)(aaaa)##x##color(white)(aaaa)##-oo##color(white)(aaaa)##-2##color(white)(aaaaaaaa)##1##color(white)(aaaaaaa)##+oo#

#color(white)(aaaa)##x+2##color(white)(aaaaa)##-##color(white)(aaaaaa)##+##color(white)(aaaaaaa)##+#

#color(white)(aaaa)##x-1##color(white)(aaaaa)##-##color(white)(aaaaaa)##-##color(white)(aaaaaaa)##+#

#color(white)(aaaa)##dy/dx##color(white)(aaaaaaa)##+##color(white)(aa)##0##color(white)(aaa)##-##color(white)(aaa)##0##color(white)(aaa)##+#

#color(white)(aaaa)##y##color(white)(aaaaaaaaa)##↗##color(white)(aa)##20##color(white)(aa)##↘##color(white)(a)##-7##color(white)(aaa)##↗#

The intervals of increasing are #x in ] -oo,-2 [ uu ] -7, oo[ #

The interval of decreasing is #[-2,1]#