The sulphate ion (SO4) has the 2- charge, not the molecule. All molecules are neutral.
As for the question, it's an ionic equation not a normal balanced equation, so we have to do things a little differently...
First write out all the reactants and products in their states:
Ba2+ (aq) + 2Cl- (aq) + 2H+ (aq) + SO4 2- (aq) --> Ba2+ (s) + SO4 2- (s) + 2H+ (aq) + 2Cl- (aq)
You need to know that BaSO4 is insoluble so the state changes from (aq) to (s).
Now you cancel out the ions that are exactly the same on each side (exactly the same means same state too).
Ba2+ (aq) +
2Cl- (aq) +
2H+ (aq) + SO4 2- (aq) --> Ba2+ (s) + SO4 2- (s) +
2H+ (aq) +
2Cl- (aq)To finish off, write BaSO4 as a molecule because it doesn't dissociate into separate ions (since it's a solid):
Ba2+ (aq) + SO4 2- (aq) ---> BaSO4 (s)