General knowledge:
* Understand
* Comprehend
* Realize
* Be aware of
* Be familiar with
* Have an idea of
* Grasp
* Recognize
* Perceive
* See
Specific knowledge:
* Be certain
* Be sure
* Be convinced
* Be confident
* Have proof
* Have evidence
* Be informed
* Be acquainted with
* Be skilled in
* Be proficient in
Informal:
* Get
* Figure out
* Catch on
* Get the hang of
* Be in the know
* Be up on
More nuanced:
* Be cognizant of
* Have a grasp of
* Be privy to
* Be acquainted with
* Be well-versed in
Literary:
* Apprehend
* Discern
* Fathom
* Ascertain
* Cogitate
* Conjecture
The best alternative will depend on the specific situation and the desired tone.