how to figure out geno and phenotypic ratios on a six trait cross.?

Question

A cross of TtBbRrnnAaff with a ttbbRRBbaaFf. How do you figure that stuff out mathmatically, without having to count each square

Answer 1

OK, this is something that you never do in real life, only in class. I guess you haven't learnt linkage yet, so you can handle all genes as independently assorted ones (otherwise you cant't soplve this anyway).
What you do is you calculate the probability of a given genotype in the next generation for each gene separatelly, and multiply these probabilities.

For example, the ratio of the genotype TtBbRrNnAaFf = 1/2*1/2*1/2*1/2*1/2*1/2 = 1/256
(Since for all genes one of the parents was heterozygous and the other homozygous, half of the progeny will be hetero for each gene.)

You can calculate the phenotypes the same way, but the numbers will be different, of course.

Answer 2

The easiest way is by algebraic multiplication. If
your traits are independently assorting (each on a
different chromosome for example) you just
determine the result for each gene pair separately
and multiply them together. For example, two
gene pairs each of which gives a 3:1 ratio by
itself: 3:1 x 3:1 = 9:3:3:1. Just do this 4 more
times for the additional gene pairs and you have
the answer. Of course the gene pairs in your
example will not give 3:1 ratios. For Tt x tt the
ratio will be 1:1, likewise for most of the others,
though there is apparently a typo in one of your
parents, so I can't tell for sure. Also you do have
to keep track of whether the alleles are pure
dominant-recessive or blending, which will affect
the phenotypes.