Quantitative Traits Genetics
Question a


The only possible genotype that brings a phenotype of 12 inches is: $AABBCC$. Similarly the only possible genotype that bring a phenotype of 6 inches is: $aabbcc$. In consequence the offsprings can only be: $AaBbCc$ which measure $2+1+2+1+2+1 = 9$ inches.


Question b


Now the question is: if we breed two $AaBbCc$ how many offsprings measure 11 inches? Because there are three bi-allelic genotypes you have $2^3=8$ possible gametes and therefore you have to draw a 8x8 punnett square. Doing so, just count the proportion of offsprings that measure 11 inches. You can reason slightly more logically and get a faster answer. To measure 11 inches you need to have only capital letters in your genome except at one position. In consequence, if your father gives the gamete $ABC$, you mother should give the gamete $ABc$, $AbC$ or $aBC$. You can inverse the role of the father and the mother and it works as well. Therefore, you have 6 possible combinations that give rise to an offspring that measure 11 inches. Because there are $8 \cdot 8 = 64$ possible combinations, the proportion of offspring that are 11 inch-long is $\frac{6}{64} = \frac{3}{32} = 0.09375 ≈ 0.1$. About 10% of your F2 individuals are 11 inch long.