First, multiply each side of the equation by #color(red)(42)#. This is the lowest common denominator of the two fractions and will eliminate the fractions while keeping the equation balanced. Eliminating the fractions with make the problem easier to work.
#((x - 4)/6) xx color(red)(42) = (3/7) xx color(red)(42)#
#((x - 4)/cancel(6)) xx cancel(color(red)(42))7 = (3/cancel(7)) xx cancel(color(red)(42))6#
#(x - 4)7 = 3 xx 6#
#7(x - 4) = 18#
Next, we can expand the terms in parenthesis:
#7x - (7 xx 4) = 18#
#7x - 28 = 18#
Then we can add #color(blue)(28)# to each side of the equation to isolate the #x# term while keeping the equation balanced:
#7x - 28 + color(blue)(28) = 18 + color(blue)(28)#
#7x - 0 = 46#
#7x = 46#
Now we can solve for #x# by dividing each side of the equation by #color(green)(7)# which will keep the equation balanced:
#(7x)/color(green)(7) = 46/color(green)(7)#
#(color(green)(cancel(color(black)(7)))x)/cancel(color(green)(7)) = 46/color(green)(7)#
#x = 46/7#
