One good strategy for multiple-choice questions is process of elimination. To apply that strategy here, look at the beaming of the eighth notes.
12/8 and 6/8 imply groups of three. That is, they are "compound" meters. The beaming does not reflect groups of three. Similarly, the longer note values are not dotted, and there are no instances where a quarter note is grouped with an eighth note. This is clearly not a compound meter, so we can eliminate those choices.
This leaves us with a choice between 4/4 and 12/4. In 4/4, no more than four eighth notes should be beamed together, but here we have a group of six. Without further analysis, we can eliminate 4/4, leaving 12/4 as the only possible answer.
At this point, we might notice that one of the facts given in the question is that the notation is described as one measure. It looks like you're supposed to consider whether bar line have been omitted, but that's not actually what they're asking. They present you with "a given measure," and all you have to do is add up the durations of the notes it contains. This is the equivalent of three whole notes, six half notes, twelve quarter notes, or 24 eighth notes.
Thus, by two independent lines of reasoning, we arrive at the same answer: 12/4.