💡 Detailed Explanation
The correct choice is 'ように' (in order that / so that). The grammar pattern 'ように' is used to express a purpose or goal when preceded by a potential verb, non-controllable verb, or negative verb ('ひかない' - not catch). Sentence translation: 'Please keep warm and sleep so that you don't catch a cold.' 'ために' (in order to) is used exclusively with active, controllable verbs (e.g. '買うために'). 'ことに' and 'ものに' are not used for expressing purpose.