Imperatives with "more" and "less"
Solution 1:
In the examples you give, moving the adverb of "more" or "less" alters what word it is modifying. Compare:
Eat less candy
Eat candy less
Either of these are grammatically correct and convey different meanings.
In the first, less is more describing candy, saying that "you should eat a smaller amount of candy". This can either in general (eg. going from eating 5 candy bars a day to 2 candy bars a week), or in the specific event this statement would be said (eg. a group is sharing a bowl of candy and one person has taken half of the candy bars for themselves).
In the second, less feels like it is describing the phrase eat candy. It is a shorter way of saying "Eat candy less [often]". It more describes the amount of candy-eating times, as opposed the amount of candy eaten (i.e. going from eating 5 candy bars a day to 6 candy bars once a week). In this sense "eating candy" is being treated as an activity, and one that someone should do less often.
When making statements like these, it then becomes important to identify whether the action you want "less" or "more" of is more of a discrete activity or a continuous habit. In the case of "washing hand" compare:
Wash more [of your] hands
Wash your hand more
The first sense sounds strange, mostly because you only have as many hands as you have (usu. two). You can't wash more of your hands. This then has a meaning toward " wash further up your arm" or "wash for more time". Note, that if the intended meaning is to do a more thorough job of washing one's hands, then Wash your hands better would probably be used.
The second sense makes sense, as more is modifying "wash" and treating "wash your hands" as an activity. It is stating that one should wash their hands more often than they currently do (eg. twice a day to 5 times a day).
For the "do more exercise" (which doen't currently make sense)" here are some options with their nuance in parenthesis.
Exercise more (exercise[verb] should be done more often or a longer period of time)
Do more exercises (do more types of excercises[noun])
Do the exercises more (do a specific set of exercises[noun] more often)
This again follows the same pattern (for simple commands) that when a modifier comes between a verb and its object, it modifies just the object (usu. in terms of degree). On the other hand if it comes after the object, typically the verb-object phrase is treated as an activity and the modifier describes how often.