Interpreting 'half of two' as 2/2=1, then adding 2 gives 3. The phrase 'half of X plus Y' is ambiguous - it could mean (half of 2) + 2 = 3, or half of (2+2) = 2, or (half of 2) + (half of 2) = 2. The answer assumes the first interpretation. This is a poorly worded question.