There's no single definitive answer to how many universities are in the Caribbean. The number depends on how you define "university" (some institutions might be considered universities in some contexts but not others, and the line between university and college can be blurry) and which islands you include in your definition of the "Caribbean".
You'll find varying numbers depending on the source, but it's safe to say there are dozens of universities and university-level institutions across the Caribbean islands. Some sources will list well over 50, others fewer.