Let's Explain the Expression andare incontro a

When you meet someone halfway on a deal, or you go towards someone who is coming towards you, say, on the street, we often use the turn of phrase: andare incontro a. 

Andare is "to go" and incontro in this case is an adverb (or preposition) meaning "toward." 

Mi puoi venire incontro?

Can you meet me halfway?        

Using this turn of phrase can be a little confusing, but here are the elements:

a verb of motion, which is usually andare (to go) or venire (to come). It might even be correre (to run).

the adverb or preposition incontro meaning "toward"

the preposition a (to)

an indirect object noun or pronoun

Let's look at some Yabla examples of how we can use andare incontro a.

The word order can change and often the indirect object comes first, as in the following examples. In this case, the preposition a is included or implied in the indirect pronoun. 

Ti vengo incontro (I'll meet you halfway).

È successo che stavo pulendo il locale e...

What happened is that I was cleaning the bar and...

poi l'ho sentita e gli [sic: le] sono andato incontro,

then I heard her and I went towards her,

ma non c'è stato verso di farla ragionare.

but there was no way to get her to reason.

Captions 2-4, Imma Tataranni Sostituto procuratore - S1EP1 L'estate del dito

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La notte, Roma, le sue luci e tu che mi vieni incontro.

The night, Rome, its lights and you coming towards me.

Captions 1-2, La Ladra - EP. 12 - Come ai vecchi tempi

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In the following example, the verb correre (to run) is used instead of andare (to go) or venire (to come), but it works the same way.

Attori, tecnici, comparse gli corrono incontro.

Actors, technicians, extras run towards them.

Caption 16, Vivere - Un'avventura di Vittorio De Sica - Part 10

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If, rather than a pronoun, I use a noun (la difficoltà) as an object, as in the next examples, then I will need the proposition a.

Vado incontro a tante difficoltà.
(I'm going to run into plenty of difficulties).

Io vado incontro al mio destino

I go towards my destiny

Caption 21, Niccolò Fabi - Lontano da me

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Io e Sua Eminenza cercheremo una soluzione

His Eminence and I will look for a solution

quanto possibile per venire incontro

as far as possible to meet you half way

a quello che Lei mi ha chiesto.

for what you have asked me.

Captions 29-31, Vivere - Un'avventura di Vittorio De Sica - Part 9

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In the next example, it's a bit different, because Nora is using the first person plural to make things sound more collaborative, but the meaning is clear. She wants a discount.

Senta, io so che Lei è un professionista, una brava persona,

Listen, I know that you are a professional, a good person,

quindi non possiamo venirci incontro un pochino sul prezzo?

so can't we meet halfway a bit on the price?

Captions 25-26, Sposami - EP 4 - Part 14

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Another reason andare incontro a can cause confusion is that l'incontro exists as a noun (the encounter) and incontrare means "to meet" or "to encounter." The first person singular of incontrare is incontro (I encounter, I meet). For more on these meanings, see this lesson: Close Encounters with Incontro.  

In addition, in is a preposition all on its own meaning "to" or "in." Contro is a preposition meaning "against."