Write 6 cubic yards as 6 yd³ and then as 6·yd·yd·yd and then as 

We could get by with just 3 unit multipliers by using 1yd = 36in,
but you are instructed to use 6 unit mutipliers, so we must not
use that, but instead use 1yd = 3ft and then 1ft = 12in

Since  has "yd"'s on top we must use a unit 
multiplier that has "yd" on the bottom to cancel with the "yd"
on top, so we use the unit multiplier , and
since there are 3 "yd"'s to cancel out we use it three times.
That's 3 unit multipliers:


···

Now you see those three "yd"'s on the bottom cancel those three
"yd"'s on the top and we have:
···

Now, as before, since that has "ft"'s on top we must use a unit 
multiplier that has "ft" on the bottom to cancel with the "ft"
on top, so we use the unit multiplier , and
since there are 3 "ft"'s to cancel out we use it three times.
That's 3 more unit multipliers:

······.

Then we cancel out the "ft"'s:

······.

Now all that's left is:

 =  = 279,936 in³.

Note that in³ means the same thing as "cubic inches".

Edwin