jmc

$6$ are blue and green - $b+g=6$ $8$ are red and blue - $r+b=8$ $4$ are red and green- $r+g=4$ We can do trial and error. Let's make blue $5$. That makes green $1$ and red $3$ because $6-5=1$ and $8-5=3$. To check this, let's plug $1$ and $3$ into $r+g=4$, which works. Now count the number of marbles - $5+3+1=9$. So the answer is $\boxed{9}.$