Optimizing a Partition Method
I'm wondering if it is the efficiency that resulted in you getting half points:


runPartition is rather an unclear name in itself;
highIndex seems to be inclusive, which is uncommon (the number of elements is now highIndex - lowIndex + 1);
counterOne and counterTwo are not good names for indices - even i and j would have been better;
it is very likely that the localArray as a field name raises some questions; why is it a field in the first place? And why is it called local if it is not local to the method?
it seems to me that you would set the counterOne to the index you want to swap and perform the decrease afterwards (possibly using -- in the call to swapValues);
the braces are at uncommon and uneven positions when it comes to Java / indentation.