Multiply everything by #x# to get rid of the #x# in the denominator:
#4/x+7=6/x#
#4/xcolor(blue)(*x)+7color(blue)(*x)=6/xcolor(blue)(*x)#
#4/color(red)cancelcolor(black)xcolor(blue)(*color(red)cancelcolor(blue)x)+7color(blue)(*x)=6/color(red)cancelcolor(black)xcolor(blue)(*color(red)cancelcolor(blue)x)#
#4+7color(blue)(*x)=6#
#4+7x=6#
#4+7xcolor(blue)-color(blue)4=6color(blue)-color(blue)4#
#color(red)cancelcolor(black)4+7xcolor(red)cancelcolor(black)(color(blue)-color(blue)4)=6color(blue)-color(blue)4#
#7x=6color(blue)-color(blue)4#
#7x=2#
#color(blue)(color(black)(7x)/7)=color(blue)(color(black)2/7)#
#color(blue)(color(black)(color(red)cancelcolor(black)7x)/color(red)cancelcolor(blue)7)=color(blue)(color(black)2/7)#
#x=color(blue)(color(black)2/7)#
That's the solution. Hope this helped!