For fun I began reading an interesting online paper I found, Spiders for rank 2 Lie algebras, and on page $5$ we have the following calculation, akin to a tensor product expansion via bilinearity:
$\hskip 0.8in$
However, I believe the $21=6+6+9$ should just be a $12=6+6$, so that $9$ appears only once in the final result as the coefficient of the second web you see. What's going on?
(Also, help on more pertinent tags would be appreciated.)