The possible blood groups of the offspring of parents with blood group 0 and AB are A and B.

Let`s break down the options to understand them better:

Option 1 suggests that the possible blood groups of the offspring are 0, A, B, and AB. This is incorrect because offspring cannot have blood group 0 if one parent has blood group AB.

Option 2 suggests that the possible blood groups of the offspring are A and B. This is the correct answer because when one parent has blood group 0, they can pass on either an A or B allele to their offspring. When the other parent has blood group AB, they can pass on either an A or B allele as well. Therefore, the possible combinations are AA, AB, BA, and BB, resulting in blood groups A and B for the offspring.

Option 3 suggests that the possible blood groups of the offspring are A, B, and AB. This is incorrect because offspring cannot have blood group AB if one parent has blood group 0.

Option 4 suggests that the possible blood groups of the offspring are O and AB. This is incorrect because offspring cannot have blood group O if one parent has blood group AB.

Therefore, option 2 is the correct answer.