The question asks for what values of A satisfy the equation, right? So yes, you've done all the hard work here, A=2 is a solution that satisfies |2x-4|<A.

But A=3 is a solution too, is it not? If something is less than 2, then it must certainly be less than 3... and 4... and 2.000000001, and indeed every number greater than 2.

Thus A>=2.