First, expand the term in parenthesis:

#-3(7n + 3) < 6n#

#-21n - 9 < 6n#

Now, add #color(red)(21n)# to each side of the inequality to isolate the #n# term while keeping the inequality balanced:

#-21n - 9 + color(red)(21n) < 6n + color(red)(21n)#

#-21n + color(red)(21n) - 9 < (6 + 21)n#

#0 - 9 < 27n#

#-9 < 27n#

Next, divide each side of the inequality by #color(red)(27)# to solve for #n# while keeping the inequality balanced:

#-9/color(red)(27) < (27n)/color(red)(27)#

#-1/3 < (color(red)(cancel(color(black)(27)))n)/cancel(color(red)(27))#

#-1/3 < n#

And to solve in terms of #n# we reverse or "flip" the inequality:

#n > -1/3#