There are many synonyms for the phrase "broad hint" which typically means a suggestion that is delivered in an indirect or subtle manner but that is still easy to understand. Some synonyms for this phrase might include "veiled suggestion", "subtle insinuation", "implied clue", or "implicit hint". Other related phrases might include "nudge and a wink", "subtle nod", "hint of something", or "suggestion that is left unsaid". No matter what phrase you use to describe this type of subtle suggestion, the idea is typically the same - it is a way of communicating something without coming right out and saying it directly.