How many moles of solid Mg(OH)2 should you add to 200mL of 0.15M lactic acid solution to produce pH 4.0 buffer?

-I don't know how to do this w/0 knowing pKa, but I don't think the point is to look up pKa. Is there some other way to solve this?

No. pKa is 3.86 I think. I looked it up on the web and I've posted the way to work the problem earlier. If you are parsing the question, the problem is asking for mols Mg(OH)2 required to produce a pH of 4.0 from that solution of lactic acid. Looking up pKa is just a part of what you need to do to get started. pKa can be calculated, of course, but not from data in this question.