explain why the method of converting units that we've used all unit is called the "factor-label" method.

It's also called dimensional analysis. its called this because it uses conversion factors that provide the link between the unit being converted and the new unit of measure.

Here's my idea on the subject.

We use conversion factors to convert a measurement in some units to an equivalent value in some other unit.

measurement in some unit * conversion factor = equivalent value in other units

Factors are numbers that we multiply together to get another number, so that accounts for the word "factor" on the name.

The units in the conversion factor are the "labels" we apply to the numbers in the conversion factor.

Hence the name, "factor-label" method.

The term "dimensional analysis" is probably more appropriate but more difficult to say.