First it would be useful to turn your fractions into improper fractions. This is so you can add and subtract them easily.
#" "3 3/4+n=6 5/8#
#[1]" "15/4+n=53/8#
Now your goal is to only have #n# on one side. We will do this by subtracting #15/4# from both sides.
#[2]" "15/4+n-15/4=53/8-15/4#
You may cancel #15/4# on the right side now, since #15/4-15/4=0#.
#[3]" "n=53/8-15/4#
You can simplify this further by combining #53/8# and #15/4#. But you will first need to make sure they have the same denominator. So multiply #15/4# by #2/2#. This is valid because #2/2=1#. Once you do this, both fractions will now have the same denominator.
#[4]" "n=53/8-(15/4)(2/2)#
#[5]" "n=53/8-30/8#
#[6]" "n=(53-30)/8#
#[7]" "color(blue)(n=23/8=2 7/8)#
