How do thermodynamics and kinetics control this reaction? 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 $k_1 &gt; k_2$ 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.