Synonyms for Put across:

n.

lay out, illustrate, interpret, define, run-through, set out, clarify, explain. put across (noun)
pass, pass on, communicate.

v.

convey (verb)
communicate, pass on.
explain (verb)
define, clarify, illustrate, interpret.
interpret (verb)
explain.

Other synonyms:

define, set out, clarify. interpret, run-through, illustrate. lay out. Other relevant words:
clarify, explain.