It depends on the organisation, but in most Taekwondo organisations, it typically takes 4 – 6 months to get to yellow belt from white belt.
In most Taekwondo organisations, yellow is the second belt colour, and white is the first. Students start training with a white belt, and later progress to a white belt with a yellow tag or stripe, and then later to a yellow belt. (Some Taekwondo organisations don’t have the intermediary belt.)
The minimum length of time that must pass before a student can grade from white belt to yellow tag is typically 2 – 3 months.
The minimum length of time that must pass before a student can grade from yellow tag to a full yellow belt is typically 2 – 3 months.
Thus, the total time it takes to go from an absolute beginner to yellow belt in Taekwondo is typically 4 – 6 months (and you have to train regularly throughout this time).
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You can find more information on this topic in the book Changheon-yu Taekwondo: Foundation Syllabus, which is a handbook for colour belt students who are training in Changheon-yu Taekwondo (ITF Taekwondo). It contains movement descriptions, floor diagrams, and relevant Korean terminology for all of the colour belt patterns.