The better solvent for separating the mixture of A and B is dichloromethane
Explanation:
Petroleum ether is the mixture of hydrocarbons obtained from the petroleum distillation with a boiling range between 35 and 60°C. Is used as a solvent.
In the other hand, the best solvent for separating a mixture in TLC is the one that has the higher difference between RF's of the compounds.
The difference in RF's in dichloromethane is:
|0.44 - 0.69| = 0.25
In petroleum ether:
|0.29 - 0.45| = 0.16
That means the better solvent for separating the mixture of A and B is dichloromethane