Start by filling in the directly given answers. Hints (1.), (7.) and (8.) give positions of ‘coal’, ‘yellow’ and ‘Erin’, and because ‘ball’ is in the yellow gift per (4.), you can fill in that as well.
Hint (9.) reveals the position of ‘Tom’. By hint (10.), there has to be a single column between Chris and Rob, meaning that Chris can only be in the first or the third column, while Rob takes the other position. Since Chris got a doll per hint (3.), he can’t be in the third column. That reveals positions of all remaining children.
Hint (4.) gives Sue’s gift color, while hint (2.) reveals Rob’s. Since ‘green’ is to the right of the ‘blue’ per hint (5.), you can complete the color row.
Hints (3.), (6.) and (12.) are used to distribute gifts and complete the puzzle.