Attention: I'm not a teacher.
Hi Claudio,
There is further explanation of the expression “put across” as a phrasal verb and an idiom.
put across = a) cause to be understood or accepted, as in
She put her views across very well.
b) attain or carry through by deceit, as in
You can't put anything across this teacher.
put across = put over
put over - make something or someone be understood or accepted, as in
The public relations staff helped put our candidate over to the public.
put over on - fool, deceive, as in
We can't put anything over on Tom.
put across - transmit information, communicate, convey a message
put across - in such a manner as to be comprehensible, acceptable, or successful: put our idea across; get a message across.
Regards.
V.