How many months of daylight does Alaska get?

12
Do you mean continuous daylight, or any daylight at all?

Alaska is very large and covers a great range of latitude, so the answer varies (a lot) depending on what point of reference you use. If, to make it most interesting, you are in the town of Barrow, Alaska (the northernmost city in Alaska), starting around May 11 or 12, the sun does not set and remains above the horizon until around July 31 or August 1. That is a period of 82 or 83 days; less than three months.

If you mean any daylight at all, then the sun sets around November 18 or 19 and remains below the horizon for about 65 days. In that case, the answer is that for only ten months out of the year does Barrow, Alaska, have any daylight at all.