"The child doesn't want to wash his hands."
Translation:El niño no quiere lavarse las manos.
Because the lavarSE implies that the boy (himself) washes the hand (which we know is his hand because of the relexive verb 'se'). So including the sus is redundant.
Thank you for your response. I understand this rule is not applied here, but do you know which rule is?
There are general guidelines (e.g. most words ending in o are masculine; most words ending in dad and ción are feminine) but no actual rules.
El niño se lava las manos <- Here the word lavarse is conjugated El niño no quiero lavarse las manos <- Here the word querer is conjugated (and lavarse isn't)