Multiply each side of the equation by the lowest common denominator, which is #(color(red)(n)(color(blue)((n - 4)))#, to eliminate the fractions while keeping the equation balanced:

#3/n xx color(red)(n)(color(blue)(n - 4)) = 6/(n - 4) xx color(red)(n)color(blue)((n - 4))#

#3/color(red)(cancel(color(black)(n))) xx cancel(color(red)(n))(color(blue)(n - 4)) = 6/color(blue)(cancel(color(black)((n - 4)))) xx color(red)(n)cancel(color(blue)((n - 4)))#

#3(n - 4)= 6n#

Next, expand the terms in parenthesis on the left side of the equation by multiplying each term within the parenthesis by the term outside the parenthesis:

#3(n - 4)= 6n#

#(3 xx n) - (3 xx 4)= 6n#

#3n - 12 = 6n#

Then, subtract #color(red)(3n)# from each side of the equation to isolate the #n# term while keeping the equation balanced:

#-color(red)(3n) + 3n - 12 = -color(red)(3n) + 6n#

#0 - 12 = (-color(red)(3) + 6)n#

#-12 = 3n#

Now, divide each side of the equation by #color(red)(3)# to solve for #n# while keeping the equation balanced:

#-12/color(red)(3) = (3n)/color(red)(3)#

#-4 = (color(red)(cancel(color(black)(3)))n)/cancel(color(red)(3))#

#-4 = n#

#n = -4#