In the first step, two moles of HCl are added to carbon carbon triple bond of propyene to form a geminal dichloride.
Chlorine atoms are added to the more substituted internal C atom. In the next step, the hydrolysis of two C−Cl bonds gives a geminal diol which then loses a molecule of water to form acetone.
For the given reaction sequence, the products (A) and (B) are CH3C(Cl)2CH3 and CH3COCH3 respectively.