What does "I would've taken you up on that" mean?

Native speaker’s answer
Rebecca
To "take up someone on something [an offer]" means to accept someone's offer or suggestion. Thus, "I would have taken you up on that [offer]" can be understood as "I would have accepted your offer [but something prevented me from doing so]." Essentially, the speaker is expressing that it would have been a possibility, but it didn't happen in the end. Ex: I would have taken you up on your offer if you told me sooner. Ex: Can I take you up on your previous offer? You said you'd help me with a small favor.