Which of the following reactions shows that the rate of the appearance of d is twice the disappearance of a and one third the disappearance of b?

First, we are discussing reversible reactions here, since the reaction is proceeded in both directions forming both reactants and products.

The reaction is symbolized as:
A + B <> C + D

The first given is:
The rate of appearance of D is twice the disappearance of A
This means that the coefficient of D in the reaction is twice the coefficient of A

The second given is:
The rate of appearance of D is one third the disappearance of B.
This means that the coefficient of D in the reaction is 1/3 that of B. This also means that the coefficient of B is 3 times that of D.

Combining these two pieces of information, we will find that the best equation that resembles this scenario is:
A + 6 B <> C + 2 D 

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