for masses A & B to accelerate ...
$\displaystyle T > 2mg\sin{\theta}$
$\displaystyle mg > T$
using these two inequalities, you should be able reach the first conclusion in the problem statement.
for the second conclusion, start with net force equations for each mass ...
$\displaystyle T - 2mg\sin{\theta} = 2ma$
$\displaystyle mg - T = ma$
---------------------------- combine ...
$\displaystyle mg - 2mg\sin{\theta} = 3ma$
solve for acceleration ...
$\displaystyle a = \frac{g(1-2\sin{\theta})}{3}$
... remember that this acceleration is only applicable for a displacement of magnitude x for both masses.
now, you finish it.