(1 foot/1) multiplied by (12 inches/foot)
The foot in the numerator cancels with the foot in the denominator, so the units of the answer is inches.
]]>As kylekatarn showed, it is only cancelling of terms in a fraction.
For example LY to m is:
1 LY × (9.46 × 10^15 m/LY) = (1 × 9.46 × 10^15 mLY/LY) = 9.46 × 10^15 mLY/LY
So the result has the units mLY/LY which is just m, because LY/LY can be cancelled (I think the interpretation of LY/LY is "Light-Years per Light Year" which is of course 1)
]]>Thanks in advance,
Wladislaw