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Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
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Even though we have 2 variables (x and y) and 0 equations, D is most likely the answer, since each condition has 2 equations. So, we should consider each condition on its own first.

Condition 1)

Since ax + by + c = 0 and bx + 2cy + 4a = 0 (abc ≠ 0) has infinitely many solutions, we have a/b = b/2c = 3/4a. Assume a/b = b/2c = 3/4a = k.
Then we have b = ak, 2c = bk and 4a = ck. When we multiply those equations together, we have 8abc = abdk^3. Since abc is not equal to 0, we have k^3 = 8 or k = 2.
Then, b = 2a, 2c = 2b, 4a = 2c. The second equation reduces to c = b, so we have b = c = 2a.
Thus both equations in the system of equations are x + 2y + 2 = 0.
We have x + 2y = -2.

Since condition 1) yields a unique solution, it is sufficient.

Condition 2)
Since the unique even prime number is 2, we have |x + 2y| = 2 which yields x + 2y = 2 or x + 2y = -2.
Since x + 2y is negative, we have x + 2y = -2.
Since condition 2) yields a unique solution, it is sufficient

Therefore, D is the answer.
Answer: D

This question is a CMT 4 (B) question: condition 2) is easy to work with, and condition 1) is difficult to work with. For CMT 4 (B) questions, D is most likely the answer.

Note: Tip 1) of the VA method states that D is most likely the answer if condition 1) gives the same information as condition 2).

If the original condition includes "1 variable", or "2 variables and 1 equation", or "3 variables and 2 equations" etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A, B, C or E.