The safe, recommended dose for paracetamol is 500mg-1g (1 or 2 tablets) every four to six hours, with NO MORE than 8 tablets being taken in any one 24 hour period.
So you are talking about double the recommended daily safe dose.
It is impossible to say how long as each person's liver processes drugs at a differing rate die to a number of factors such as age, gender and predisposing medical conditions.
It could be as quick as within 24 hours or take a few days.
Paracetamol is one you really don't want to exceed the dosage on. As little as four tablets a day increases the risk of complications. you need more information before you can get any sort of answer about toxicity especially the weight of the victim. Hagrid could put away a lot more than Dobby for example.
generally there will be no symptoms at all until 4+days later when jaundice will be exhibited and unfortunately at this point there will be irreparable partial or total liver damage
however if one even suspects an 'overdose' there is a risk free 'antidote'
aspirin is a far far safer drug (if one does not have a troubled stomach or flu and young) in cases of accidental or unknowing overdose
BUT THERE IS 'NO MONEY' (PROFIT) IN ASPIRIN SO THAT IS WHY THE MEDICAL OPPRESSION (SIC) 'PUSHES' PARACETAMOL (ACETAMINOPHEN)