1. Convey Board games are more than kid games
This will be the most challenging task since you're trying to break through a common stereotype playing games with a single flyer. You're not going to be able to convince anyone to change their preconceived ideas of what the image playing games portrays, so instead, associate board games with another common scenario that gives a different impression.
Chess is probably the most universally regarded board game that is "sophisticated" and smart enough to earn the respect of most "adults". So I'd suggest using chess pieces on the flyer to direct people's notion of kids to strategic mastery and pique their interest and curiosity by saying there are other board games (most of which non-gamers will never have heard of before) that are just as sophisticated and strategically challenging (and even a whole lot more fun) as chess.