The question says they don't responds to antacids THEN asks which you to identify which drug is the most effective at suppressing acid production, NOT what the most effective antacid is. The answer is PPI's.
I will say, however, I was looking for something like octeotride.
This patient is unresponsive to many antiacids. They dont specify which ones, but the question is basically asking which antiacid is the strongest. That would be PPIs, which inhibit gastric H K ATPase