When forming the plural of 'spoonful', the suffix '-ful' is treated like a regular noun ending, so we add '-s' to make 'spoonfuls'. This follows the pattern of 'handfuls', 'cupfuls', etc. 'Spoonsful' would mean multiple spoons each full of something, which changes the meaning. 'Spoonfully' and 'spoonfuly' are not valid word forms.