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If Benedict was true, then there are only two true statements, Benedict's and Bob's, because Brian would be lying, so would Brenda, and Billy. Bob and Brian's statements cannot be both true either. If Bob's statement was true, it would get us tangled and we would not find out if there were three truths. If Brenda's statement was true, then we are still unsure. If Brian's statement was true, then there would only be two truths. If Billy's statement was true, you would find three truths. One is that Benedict was lying, another one that the gift was in the red box, and that the gift was not in the blue box.

If Benedict is true, then Bob has to be true. But, if this happens, neither Brenda , Brian or Billy can be true.

Brian and Billy have contradicting statements which can never be true together.

If Brenda is true then either one of the contradictions AND Bob have to be true. But, this can't happen if Brian is true.

Therefore, the box belongs to Brenda

Look at the statements on the green and red boxes. One of them has to be true while the other, false as they contradict each other, Now look at the statements on the blue and orange boxes. Due to the contradicting statements again, one has to be true, the other false.

We do not know exactly which 2 statements out of these 4 are true, but we know that there have to be EXACTLY TWO true statements here. But since there are THREE true statements, the third statement of truth has to be the one on the yellow box since that is the only statement left. Now it is obvious that Mrs Tan's gift is in the red box which belongs to $\boxed{Brenda}$ .