There are four binary choices, y/Y and r/R for each of two parents, and all $2^4=16$ ordered combinations of these choices are being produced with equal probability. However, you want to count unordered combinations. Since there are three unordered combinations for each feature (YY, Yy, yy, and RR, Rr, rr, respectively) which can all be combined with each other, there are $3^2=9$ unordered combinations. The mixed combinations, Yy and Rr, correspond to two ordered combinations each, whereas the pure ones, YY, yy, RR and rr, correspond to one ordered combination each. Since it's the ordered combinations that are equiprobable, you get a factor of $2$ for each mixed feature. Thus the frequencies are:
YYRR: $1\cdot1=1$ YYRr: $1\cdot2=2$ YYrr: $1\cdot1=1$
YyRR: $2\cdot1=2$ YyRr: $2\cdot2=4$ Yyrr: $2\cdot1=2$
yyRR: $1\cdot1=1$ yyRr: $1\cdot2=2$ yyrr: $1\cdot1=1$