. Genes at loci f, m and w are linked, but their order is unknown. The F1 hetero

Since FMW and fmw are the most frequent phenotypes, they're the parentals.  The least frequent phenotypes are the two that are the double recombinants, depending on gene order (loci position).

a) If locus f is in the middle, our genes look like this:

Let's rearrange the parentals as MFW and mfw
m-------f-------------w
MfW and mFw are the double recombinants, therefore they will be least frequent with this arrangement.
Note: to find the double recombinants for MFW - since MF are both dominant, the recombinant would be one dominant and one recessive (either Mf or mF), and since FW are both dominant, the recombinant would be one dominant and one recessive (either fW or Fw).  Putting that together, the double recombinants are as listed, MfW and mFw

b) If locus m is in the middle, our genes look like this:
Let's rearrange the parentals as FMW and fmw
f-------m-------------w
FmW and fMw are the double recombinants, therefore they will be least frequent with this arrangement with the same logic as above.

c) If locus w is in the middle, our genes look like this:
Let's rearrange the parentals as FWM and fwm
f-------w-------------m
FwM and fWm are the double recombinants, therefore they will be least frequent with this arrangement with the same logic as above.

d) When genes are linked, they do not assort independently as Mendel's second law states.  Also, if there were a recombination frequency of 0, the parents would always pass along their phenotypes, FMW and fmw.  However, because (it seems) that RF > 0, there is a chance that there is recombination occurs.  Therefore, instead of the normal 50% chance of donating a specific gene to offspring, there becomes a higher chance because of gene linkage.  Again, because RF > 0, that is not 100% certain.  The RF is the likelihood that the genes will give a non-parental makeup. 

Here's what happens in linked genes:
The two parentals are the most common.
There are 4 classes of single recombinants that are much less common (typically) than the parentals.  The frequency of recombination depends on the gene distance in map units from one another.
There are 2 classes of double recombinants; these are the least common.  The reason for this is that their likelihood is subject to the product rule of probabilities: their probabilities are equal to the product of the RFs of the single recombinants (which are decimals between 0 and 1, therefore, multiplying the two gives an even smaller probability than either of the single RF probabilities for the single recombinants).