The two friends have come to different conclusions because in the first statement
n=4 meaning that 2n+3 equals 11 yet 4+10=14 meaning n+10 is larger yet in the latter statement n=10 this solely means that 2n+3 is larger. This then leads you to conclude that it is dependent on the amount of n, this tells you if n equals an amount totalling 8 or over 2n+3 is larger yet if n=7 they total an equal amount, this can be seen in the graph below.
Proceeding that, I found that with the expressions 3(2n+2) and 2(3n+3) they always total an equal amount due to the sole fact that you add the number which you multiplied n by. These two numbers are 2 and 3 yet now you've added two you times by three and if you add 3 you times by 2 this then leads to an equal amount.