The previous answer was well-researched, but it completely missed the point.
The issue is a bit complicated, because "time zone" can have two different meanings. If you divide the globe into 24 evenly-spaced zones of longitude and give them designations - the basis for Coordinated Universal Time, or UTC - then it is true that the State of Alaska covers four of those zones; but most people use the phrase "time zone" to mean an area in which there is a single uniform OFFICIAL time, like Eastern or Central. For political and geographic reasons, these official time zones tend to follow state and national boundaries, not the longitude lines on a map.
In fact, Alaska used to have four official time zones, but in 1983 it was decided to put the whole state on a single uniform time, except for the most distant (and uninhabited) portion of the Aleutian Islands. This causes some anomalies as you travel West - for instance, the sun and the clocks are properly synchronized in Juneau, but an hour off in Anchorage.
But there is another wrinkle. The question was not whether Alaska spans four time zones, but whether its UNIVERSITY covers the same range. U of A has three campuses (Juneau, Fairbanks, and Anchorage) which fall into just two of those evenly-spaced zones - UTC -09:00 and UTC -10:00 - and in fact they are barely one zone width apart, if you look at the actual longitudes of Juneau (134.6) and Anchorage (150.0). So the University spans at most TWO time zones, and if you consider the fact that the whole State is now in a single official zone, the correct number would probably be "one".
Posted 202 day(s) ago