how do you times cents by miles? for instance 55.5 cents x 103.9 miles?

They might mean cents/mile

Like

Sam uses his his car for work.  He gets reimbursed 55.5c/mile.  how much reimburement will he get if he drives 103.9 miles?

Ans: 

$$$\frac{55.5c}{mile}\times $103.9 miles\\\\ The miles cancel out leaving\\\\ 55.5*103.9 cents$$

$${\mathtt{55.5}}{\mathtt{\,\times\,}}{\mathtt{103.9}} = {\mathtt{5\,766.45}}$$

5766cents = $57.66

Cents are currency and miles are distance. Multiplying them wouldn't make sense.