The New York Times Connections puzzle for January 2, 2024 (Puzzle 936) features four categories: writing actions, performance terms, measurement standards, and altered vegetable names. Players must group four words into each category, with the game allowing four mistakes. Hints were provided for each category, including 'Get me a pen' for writing, 'Hokey' for performance, 'This is a level to meet' for measurement, and 'Garden produce, with a twist' for vegetable wordplay.