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Combinatorics Difficulty 4.0 AIME Find the answer United Kingdom

Adrian teaches a class of six pairs of twins. He wishes to set up teams for a quiz, but wants to avoid putting any pair of twins into the same team. Subject to this condition:

i) In how many ways can he split them into two teams of six?

ii) In how many ways can he split them into three teams of four?

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Source: UK Mathematics Trust, licensed © UK Mathematics Trust; question papers published free at bmos.ukmt.org.uk. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.