I will preface this by saying that this is only my understanding and you should probably seek specialist advice.
Assuming he abandoned his job 4 days after you paid him two weeks in advance, that means he has been overpaid by 6 days. However, his accrued leave is more than 6 days, so technically you probably still owe him 1 - 2 day's pay (depending on how many hours constitutes a day's leave).
I suspect this was roughly calculated by the employee.
Unfortunately I believe your only recourse regarding him not working out his notice period is to sue him for breach of contract and/or take out an injunction to prevent him from starting his new job until his notice period has ended, although you would then have to pay him for that period.
In most cases such legal action is not worth it. The only times I know of this type of legal action being taken is when the employee has a long notice period (say 3 months) and is in a commercially sensitive job, such as investment banking, where there is probably a "gardening leave" clause (you are paid to stay at home and not work for anyone else).
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