Translation:I am going to introduce you to my girlfriend.
This sentence means that the girlfriend is the one being introduced. The exact same sentence could also mean that the person is going to introduce you to his girlfriend, but that's not very normal unless the girlfriend is not there so that is the only meaning you can give it. When someone whants to introduce you to another person they'll normaly tell you "Ven para que conozcas a mi novia."
Clawerdinvander, your examples are wrong in many ways.
"Te voy." You are the one being introduced not the girlfriend being introduced. I made the same mistake you did and my wife explained putting 'Te' before the verb means 'You' are the one receiving the action of being presented.
Makes sense to me the way she explained it. Hope it helps.
There also was a sentence in an earlier lesson "No vas a presentar a tu madre?" translated with "are you not going to introduce your mother?" Since "te" could be 3. OR 4. case and "mi novia" doesn't give a hint on the case, it is confusing to me who is introduced to whom here...
The indirect object pronoun is required and te is the only pronoun (which looks the same for indirect object as for direct object) so mi novia must be the direct object with the personal a. (If it were the indirect object, then the sentence would be "Le te voy a presentar a mi novia." http://spanish.about.com/od/Ovrviews/a/pronouns-objects.htm
I made the same mistake. I looked up the verb presentar and "to present" was one of the definitions. I'm not going to report it though because Duolingo seems to try and narrow the correct answers down to fewer, more specific meanings. I think if they didn't do this, then it would be more difficult to learn.
Almost a year ago, did you get the answer to this yet? "I am going to present my fiancée (direct object) to you (indirect object)." The indirect object must always precede the verb, but the direct object does not need to. The 'a mi novia' uses the persanal 'a.' Think that's right. :)
I can't vouch for the truth of this, but here's a possible source of confusion:
'When there are two person objects in a sentence as direct and indirect object, a Spanish sentence drops the personal "a" before the direct object and uses "a" in front of the indirect object.' https://www.englishspanishlink.com/learn-spanish/grammar/five_min_prepositions_4_personal_a.htm
Assuming for the moment that this rule is true, let’s look at the implications. Begin with the simple sentence "Voy a presentar a mi novia." In this case I think we all understand "mi novia" to be the direct object introduced by the (untranslatable) personal a. Thus the translation is "I am going to introduce my girlfriend." Now, let’s add "te" into the mix: “Te voy a presentar a mi novia.” At this point we have to re-analyze the entire sentence. The pronoun "te" by itself is ambiguous: it could be a direct object or an indirect object. The key to the translation is how we interpret the phrase "a mi novia." It LOOKS just like the direct object phrase in the first example, but it is different. Because the sentence now has two objects that are people there can be no personal a. Therefore the "a" in "a mi novia" must be interpreted as the preposition "to" which makes "mi novia" the INDIRECT object. That leaves "te" to be the DIRECT object, hence the translation is "I am going to introduce you to my girlfriend."