That's one of Tom Hanks' first-ever questions to Andrew Luck ... straight-up wondering how much the Indianapolis Colts QB has been made fun of in his life.

Don't worry ... Luck played off the awkward question well -- "It goes both ways!" -- and the two had a pretty fun first encounter Wednesday nonetheless.

Hanks and Luck were together for an event at The Children's Museum of Indianapolis ... when Hanks revealed he's a big Luck fan -- telling the QB, "I love watching you play."

The two talked for a while ... discussing everything from Indianapolis, to social media to dealing with haters. Tom was a co-host on NBC's 'Today' Thursday ... a special spotlighting Elizabeth Dole's Hidden Heroes' campaign.

They even posed for a pic too ... and the caption the Colts wrote for it couldn't have been more perfect -- "Andy and Woody."