Genetic cross Q multiply LlGg by LlGg?

The gametes of LlGg are LG, Lg, lG, and lg.  The Punnett square is a 4x4.  Information on how to make the Punnett square can be found online or in any Biology text.

It is a dihybrid cross and you eventually get a 9:3:3:1 phenotypic ratio. You will get this same ratio for all Mendelian heterozygous crosses. You could make a Punnett square to do the problem, but there is a faster (and IMO easier way). I simply list all the genotypes of the gametes, and then calculate what proportion of offspring that genotype makes up. For this problem there are 9 gamete genotypes:
1. LLGG Chance is: 1/4 x 1/4= 1/16 (there is a 1/4 chance of getting LL from the L locus and 1/4 chance of getting GG from the G locus).
2. LLgg, Chance: 1/4x1/4=1/16
3. llGG, Chance: 1/4x1/4=1/16
4. LLGg, Chance: 1/4x1/2=1/8
5. LLgg, Chance: 1/4x1/4=1/16
6. LlGG, Chance: 1/2x1/4=1/8
7. LlGg, Chance: 1/2x1/2=1/4
8. llgg, Chance: 1/4x1/4=1/16
9. llGg, Chance: 1/4x1/2=1/8

Then you simply add up the genotypes that would lead to a double dominant phenotype (LLGG,LLGg,LlGG,and LlGg for a total of 1/16+1/8+1/8+1/4=9/16). For single dominant phenotype (llGG,llGg, and the other single dominant LLgg and Llgg you get 1/16+1/8=3/16 for both). Finally for double recessive phenotype (llgg) you get 1/16).

Therefore you have a 9 double dominant phenotype: 3 single dominant phenotype: 3 single dominant phenotype: 1 double recessive phenotype ratio.