You're in geometry, but this is algebra. 
Do you remember any algebra?

n stands for an unknown number

3n + 3 = 2n + 6

There are 2 terms on the left, 3n and 3 
3n is a "letter term" and 3 is a 
"plain number" term.

There are two terms on the right, 2n and 6
2n is a "letter term" and 3 is a "plain number"
term.

We want ONLY "letter terms" on the left
and ONLY "plain number" terms on the right.

We get rid of the number term 3 on the left
by subtracting 3 from both sides like this:

3n + 3 = 2n + 6 
   - 3      - 3
---------------
3n + 0 = 2n + 3

We can eliminate the "+ 0" and just have

    3n = 2n + 3

Now we get rid of the letter term 2n on the right
side by subtracting 2n from both sides like this:

    3n = 2n + 3
   -2n  -2n 
   ------------
    1n =  0 + 3

We can eliminate the 0 and have
 
    1n = 3

Now we can eliminate the 1 because there is
no difference between n and 1n.  So we can
just write

     n = 3 

This is algebra you're doing,
not geometry, but there is algebra in
geometry.

Edwin