"The father wants to give the spoon to the girl."
Translation:Ο πατέρας θέλει να δώσει το κουτάλι στο κορίτσι.
The first hint shows "to the girl" = "προς το κοριτσι", but it was not applicable to this sentence.
That's hints for you. They're like dictionary entries, and may contain items that are not applicable to the sentence you're currently on.
You can never rely on them to be "suggestions" or "recommendations".
mizinamo is right!δίνει indicates that it is an action that father wants to do repeatedly. Let me give you some examples. 1)Father wants to give his salary to charities. Ο πατέρας θέλει να δώσει το μισθό του σε φιλανθρωπίες. (he wants to give his salary once-υποτακτική αορίστου) 2)Father likes giving his salary to charities. Στον πατέρα αρέσει να δίνει το μισθό του σε φιλανθρωπίες. (he generally likes to give his salary to charities-υποτακτική ενεστώτα).
So δώσει indicates something that happens in one moment, whereas δίνει indicates something that happens repeatedly.
I think that would imply that he wants to do it regularly or habitually.
It's the same verb, just a different tense - present subjunctive instead of aorist subjunctive.
In the subjunctive, the present tense usually indicates habits or continuous action, the aorist a one-time occurrence, so it's more an aspect distinction than a tense distinction.
Is μπαμπάς not also acceptable here? https://screenshots.firefox.com/JZcsIkAvM8kpjCEO/www.duolingo.com If not why not? I realize it's less formal but it's not actually wrong is it?
Isn't it accusative after give?
For the direct object, yes.
Which is why you have the neuter accusative το before the neuter noun κουτάλι.
τον would be masculine accusative.
Remember that with the neuter gender, the accusative always looks like the nominative, in all Indo-European languages that I know of. (Even English has "he/him" and "she/her" but neuter "it/it".)