Can I run TwIL-LM3-Pro on an RTX 4060 Ti 16 GB?

Yes

Its published weights (7.32 GB) fit in the 14.4 GB an RTX 4060 Ti 16 GB can use, with room for ≈ 84K tokens of context.

hf download webAI-Official/TwIL-LM3-Pro

Files and context on RTX 4060 Ti 16 GB

Each file of TwIL-LM3-Pro (and of GGUF versions the site has analyzed), and how much context fits next to it, with the context cache in 16-bit or 8-bit.

TwIL-LM3-Pro on other hardware

Popular models that run on RTX 4060 Ti 16 GB

Assumes 90% of the card's memory is usable and at least 4K tokens of context for one conversation, with the context cache in 16-bit unless noted. Fits leaves at least 20% of that memory for context; Tight leaves less.