'qu'il m'a donnée pour mon treizième anniversaire.' - the link you provide with this question, 'special cases of past participle agreement with avoir' describes that, in passé composé with avoir, the past participle must agree with the object when the verb is preceded by a direct object, but also explicitly states that the rule does not apply to indirect objects. Is not 'me' in this case an indirect object (he gave it to me)?
Freeform Writing Exercise B2
The phrase is ‘donner qqc à qqn’.
The ‘qqc’ is ‘que’ (whatever noun that represents) and is the direct object, preceding the verb - and agreement of the past participle is with the gender and number of the noun represented by ‘que’.
The ‘à qqn’ is represented by the indirect object pronoun ‘me’, which also precedes the verb, but has no impact on agreement of the past participle in any situation.
When to use que to say whom / which ot that (relative pronouns)
Maarten is correct. The agreement is with "que" which refers to "la boite à outil" - which is feminine ; and not with "m' / me" which is feminine and referring to the daughter.
I hope this is helpful.
Bonne journée !
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