let's look at the first one: -4 ∈ X:
if you subtract: 6-4,you get 2 and from the recursive case we get that 2 ∈ X.
now subtract: 2-6,and you get -4 and again from the recursive case you get that -4 ∈ X.
the third case can be done similarly,maybe just with more subtractions.
but,for the second case you have to state that there is no way to get an odd number by subtracting two even numbers.to understand this try doing applying this to prove that 3 ∈ X is not true.insted of three you can use any odd number.