Well, there are two possibilities. Either each card has a number one one side and a letter on the other, or each side has either a number or a letter.

The simplest way to remove the cards and focus on truths.

if A then B

Then divide the cards into those for which A is true, and B is possible but unknown, those for which B is true but A is possible ut unknown, and others for which either A is known to be false or B is known to be true. This is of course, dependant on the ambiguity I noted above and resolve below.

If each card had exactly one letter and one number:

Two cards, the A and the 4

A: Needs to be checked, because iff the number on the other side is odd, the rule is true

K: Does not need to be checked, because if the number on the back is even or odd, the rule is true.

3: Does not need to be checked, because the rule is not iff, so if the letter on the back is vowel or nonvowel, the rule is true.

M: Does not need to be checkd for the same reason as K

4: Needs to be checked because iff the letter on the back is a nonvowel the rule is true

If each side can have a leter or a number, and each card can thus have 0, 1, or two letters:

Four flips are needed, A, K, M, 4

A: Needs to be checked, because iff there is an odd number on the other side, the rule is true

K: Needs to be checked, because iff there is not a vowel on the other side, the rule is true

3: Does not need to be checked because if there is an odd number, an even number, a vowel, or a nonvowel on the other side, the rule is true

M: Needs to be checked for the same reason as K

4: Need to be checked for the same reason as K

Because data analysis traditionally resolves ambiguities of this type towards the chaotic (assuming lack of order unless order is defined), Four would most likely be the correct choice.