Jason is packing a large box with smaller shoe boxes. The larger box has a volume of 5832 cubic inches. Each shoebox measures 12in x 6in x 5in. About how many shoeboxes will Jason be able to fit in the large box?

Volume of large box = 5832 in^3
Volume of shoe box = 12*6*5=360 in^3

Maximum number of shoe boxes that might fit in the large box 
= 5832/360 = 16.2, or 16.

However, we have to verify the dimensions to make sure each side fits.
For example, if the large box is 18x18x18=5832 in^3,
then we can only fit, along each dimension:
18/12=1.5 => 1 (6 inches remaining)
18/6=3     => 3 (0 inches remaining)
18/5=3.6  => 3 (3 inches remaining)
That make 9 boxes.
However, we still have a gap of 6 inches that we can fit shoe boxes vertically, i.e.
6/6=1 row
18/12=1 row
18/5 = 3 rows
That will fit 3 more boxes for a total of 9+3=12 boxes (instead of 16 boxes).

So 16 is the MAXIMUM number of boxes (according to volume).
The actual number of boxes will depend on the dimensions of the large box.  18x18x18 was given just as an example.

If further explanations are needed, please post in comments.