Can anyone help explain how to do this problem. i am not sure what im doing wrong. thanks

4(2n+1)=3(6n+3)+1

8n+4=18n+9+1
8n-8n+4=18n-8n+10
4-10=10n+10-10
not sure what to do.

Your are on the right track.

You want to get just the variable on one side of the equation. You have done that.
Your last step above:
4 - 10 = 10n + 10 - 10
The +10 and - 10 on the right cancel
4 - 10 = 10n
Subtract 10 from 4 on the left.
Then you something on the left = 10n.
Divide both sides by 10 to find n.