To perceive directly with the intellect

• ken
• know
• grasp
• fathom
• comprehend
• compass
• apprehend

To perceive and recognize the meaning of

• ken
• twig
• dig
• savvy
• take-in
• take
• sense
• see
• read
• make out
• grasp
• get
• follow
• fathom
• conceive
• comprehend
• compass
• catch
• apprehend
• accept

To arrive at (a conclusion) from evidence or reasoning

• judge
• infer
• gather
• draw
• deduct
• deduce
• conclude

To comprehend

• get the idea
• get the hand of
• be with it
• read-between-the-lines
• dig
• get the point of
• catch on
• get the gist of
• get
• savvy
• register
• make out
• see-the-light
• come to one's senses
• be informed of
• possess
• penetrate
• get at the root of
• get-to-the-bottom-of
• be instructed in
• have knowledge of
• experience
• have-been-around
• become alive to
• be apprized of
• make sense of
• make out
• induce
• deduce
• infer
• distinguish
• read
• discern
• realize
• ween
• wot
• have cognizance of
• be conscious of
• note
• catch
• see-into
• ken
• find out
• learn
• see-through
• cognize
• interpret
• explain
• grow aware
• recognize
• sense
• be aware of
• conceive
• master
• follow
• appreciate
• perceive
• know
• identify with
• take (one's meaning)
• seize
• figure out
• grasp
• take-in
• fathom
• apprehend
• comprehend

To suppose

• surmise
• conjecture
• guess

To accept

• count on
• take-for-granted
• concede