If you double the concentration, you'll double the amount of OH- ions (NaOH). So basically, doubling the concentration is the same as doubling the volume here. This means there is enough OH- ions to neutralise the acid in B (since there is equal moles of the ethanoic acid and sodium hydroxide and it is a 1:1 ratio; NaOH + CH3COOH ----> CH3COONa + H2O).
In A, half of the H+ ions will be able to react, but half will still remain (since NaOH is half the volume but same concentration), leaving the system in equilibrium and slightly acidic, with approximately equal amounts of the salt and the acid i.e. a buffer solution. If you need an explanation on how buffer solutions work, feel free to ask.