Let's rewrite the inequality
#6w^2-w-6<0#
Let's factorise
#(3w-5)(2w+3)<0#
Let #f(w)=(3w-5)(2w+3)#
Now, we can build the sign chart
#color(white)(aaaa)##w##color(white)(aaaa)##-oo##color(white)(aaaa)##-3/2##color(white)(aaaa)##5/3##color(white)(aaaa)##+oo#
#color(white)(aaaa)##2w+3##color(white)(aaaaa)##-##color(white)(aaaa)##+##color(white)(aaaa)##+#
#color(white)(aaaa)##3w-5##color(white)(aaaaa)##-##color(white)(aaaa)##-##color(white)(aaaa)##+#
#color(white)(aaaa)##f(w)##color(white)(aaaaaaa)##+##color(white)(aaaa)##-##color(white)(aaaa)##+#
Therefore,
#f(w)<0# when #w in]-3/2, 5/3 [#