Can I run gemma-4-12b-it-GGUF on an RTX 4060?

Yes

Its Q3_K_M file (5.69 GB) fits in the 7.20 GB an RTX 4060 can use, with room for ≈ 6K tokens of context.

ollama run hf.co/unsloth/gemma-4-12b-it-GGUF:Q3_K_M

Files and context on RTX 4060

Each file of gemma-4-12b-it-GGUF (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.

gemma-4-12b-it-GGUF on other hardware

Popular models that run on RTX 4060

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.