The answer is A, but how is that? I know B is an intermediate, so that after short time it will be bigger than C, but what does "thermodynamic control" and "kinetic control" mean?
Initially no B and C exist. At short times as $k_1 > k_2$ production of B is favoured over C. (The initial amounts of B and C are so small that back reactions can be ignored wrt. forwards ones.) At long times equilibrium constants matter and as the equilibrium constant $K_2$ is greatest this is favoured to produce C over B.
A kinetic product arises when the reaction is not supplied any additional conditions..therby proceeds through a stable intermediate. A thermodynamically controlled reaction is one where you supply heat or any such necessary condition to get a specific product ( mostly the more substituted one...ie saydseff products)...thus goes for a stable product even if a not so stable intermediate forms in the mechanism. I guess thats about it
P.S:Saydseff for organic reactions..idk what you call it in inorganic chemistry