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