Let's rewrite and simplify the inequality
We cannot do crossing over
#6/x<2#
#6/x-2<0#
#(6-2x)/x<0#
#(2(3-x))/x<0#
Let #f(x)=(2(3-x))/x#
Let's build the sign chart
#color(white)(aaaa)##x##color(white)(aaaa)##-oo##color(white)(aaaaaa)##0##color(white)(aaaaaaa)##3##color(white)(aaaaa)##+oo#
#color(white)(aaaa)##(x)##color(white)(aaaaaa)##-##color(white)(aaaa)##||##color(white)(aaa)##+##color(white)(aaaa)##+#
#color(white)(aaaa)##(3-x)##color(white)(aaa)##+##color(white)(aaaa)##||##color(white)(aaa)##+##color(white)(aaaa)##-#
#color(white)(aaaa)##f(x)##color(white)(aaaaaa)##-##color(white)(aaa)##||##color(white)(aaa)##+##color(white)(aaaa)##-#
Therefore,
#f(x)<0#, when # x in (-oo,0) uu (3,+oo)# graph{(6/x)-2 [-22.81, 22.8, -11.4, 11.42]}