Since Jill's basket can hold twice as much as Jack's, and Jack's is capable of holding 12 apples in total, this means Jill's basket can hold 12*2=<<12*2=24>>24 apples in total.
Since Jack has 4 less than the maximum amount of apples he can fit in his basket, this means Jack has 12-4= <<12-4=8>>8 apples in his basket.
Therefore, Jill's basket can hold 24/8= <<24/8=3>>3 times the amount of apples Jack is currently carrying.
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