hao3 is the combination of . The first component is nü which means 'girl' or 'female'(a figure of a women sitting with her legs crossed) and the second component is zi which means 'son' or 'offspring' (an infant with arms outstrected). One interpretation is that to have one daughter and one son is a good combination. Other meanings of hao include 'fine', 'kind', 'convenient', and 'quite'.
hao3kan4 means 'good looking' and literally translates as 'good'-'to see'.
kan4 is made up of where the first character is shou3 meaning 'hand' and the second character mu4 meaning 'eye' (the respective ancient graphic forms were ). When you hold your hand over your eye (across your brow) you are trying to look at something.
hao3chi1 means 'good to eat' and literally translates as 'good'-'eat'.
chi1 has as its components. The first character is kou3 'mouth' and the second character is qi4 meaning 'to beg' or 'solicit'. When you solicit food for your mouth, you are about to eat.