what do you mean she will be (i suppose you meant to write) short of two sweets? meaning the last child would only get 2 sweets if she tries to give everyone 4?

If so, let x be the number of children. Then we know she has 2x + 4 sweets. as she has 4 more than double the number of her children, by the second sentence. however, she has 2 less than 4 times the number of her children, so she also has 4x - 2 sweets. since this describes the same amount, we want

2x + 4 = 4x - 2

now find x