"Braucht ihr diese Tasse?"

Translation: Do you need this cup?

[EltonFreitas9]

Can the same sentence mean: Does she need this cup?

[MortiBiRD]

No, it can not. Does she need this cup? Braucht sie diese Tasse?

She goes to school. Sie geht zur Schule.

You go to school. Ihr geht zur Schule.

Her father goes to school. Ihr Vater geht zur Schule.

He gives her a pencil. Er gibt ihr einen Bleistift.

So her-(possessive pronoun) becomes ihr-(possessive pronoun)(or inflection of ihr). Her father = ihr Vater, her mother = ihre Mutter.

Her (personal pronoun) that describes an object becomes also an object in german. Depending on the verb the kasus of the object is determined. So the personal pronoun will be either sie (Akk), ihr (Dat) or ihrer (Gen).

I see her. Ich sehe sie. (most verbs will have an Akk.)

I help her. Ich helfe ihr. (a few, but some of them are common like to help, use a Dat.)

I commemorate her: Ich gedenke ihrer. (very few and most of them are rare use a Gen.).

[JonnaNono]

Reported that "Do you need this mug?" should be accepted

[cloudcomput]

Why is it "ihr" and not "sie"?

[JonnaNono]

Both 'ihr' and 'sie' (singular, she) take the conjugation 'braucht' of the verb 'brauchen' http://conjugator.reverso.net/conjugation-german-verb-brauchen.html
Here, the person who made the exercise has wanted to use the plural you, and therefore it is 'Braucht ihr' = 'Do you (all) need".
If, however, you're thinking of 'sie' in plural, that would be 'Brauchen sie' = "Do they need'.

[joanlamt]

is tasse mas/fem? is it accussasive/dative?

[EricPatter408720]

This is the collective you in this sentence, correct? Seems like an odd sentence to be asking a group of people if they need this one cup.