
Give to understand
Lead someone to believe / Have someone to believe / Try to fool someone

Dare a credere a qualcuno 
Dare a intendere a qualcuno / Far credere a qualcuno
Lead someone to believe / Have someone to believe / Try to fool someone

Dare a credere a qualcuno 
Dare a intendere a qualcuno / Far credere a qualcuno
Examples
How come you have so many books from the library? I was given to understand that you could check-out only two books at a time
Come fai ad avere tanti libri della biblioteca? Mi era stato fatto credere che si potessero prendere solo due libri alla volta
What you are saying is not true: who are you trying to fool?
Quello che dici non รจ vero: a chi vuoi darla ad intendere
The contractors were late on the project, but they had me to believe that they were waiting for a permit
L'impresa era in ritardo con i lavori e mi hanno dato a credere che stavano aspettando un permesso dal comune