Il a pris ma main specifies it was your hand he took; il a pris la main doesn't. As the lesson you linked notes, appropriate possessive pronouns are used when required to clarify whose body part is being referred to. Le/la/l'/les are used when referring to the verb's subject(s) doing something with his/her/its/their own body part/vêtements etc. With other people involved, or with the body part itself as the verb's subject appropriate possessive pronouns are used for clarity Special cases when you use mon/ma/mes/etc with parts of the body (French Possessive Adjectives)

Thanks that clears my doubt