By going by the hints at the bottom of the screen.
They are a bit vague, but hopefully in multiple replays you can figure out which is what. They're intentionally vague to make the game a bit harder.
Viewing post in Fate of the Deliveryman comments
There's "vague", then there's "Nostradamus", then there's Horoscopes, then somewhere waaaaay further along the scale are the hints from this game. And that scale might be logarithmic.
I finally beat it because I got 5 bananas and everyone who wanted one said "Potassium". Because apparently a clue referring to yellow isn't a banana (even when the only yellow thing in my inventory is a banana), and something about a nice curve isn't a banana when the only curved thing in the inventory is a banana.
Graphics are pretty cute though.