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I just started learning German language. I started to learn some very common phrase of sentences. One of such sentences is

Was machen sie?

Which basically means "what do you do?". Now, my question is if this sentence has the same meaning and implication as the English variant "what do you do". We know that the English variant can be used as a greeting.

Does that German sentence carry with it a meaning "how are you?"

No

"Was machen sie?" simply means

What are they doing?

And "Was machen Sie?" means

What are you doing?

Note the difference between "sie" (they) and "Sie" (you).
^{Side note: "Was macht sie?" (verb in singular form) means "What is she doing?"}

There is absolutely no greeting connotation in those questions. It would be very impolite to enter a room and ask this question without greeting. Asking this question means to demand accountability.

But there are questions that contain greeting connotations:

Wie geht es dir?

Wie geht es Ihnen?

(often "geht's" instead of "geht es", i.e. "Wie geht's dir?")

This means:

How are you?

But in the German question the greeting connotation is weaker than in the English sentence. So, you more often will hear an explicit greeting before this question:

Servus, wie geht es dir?

Guten Abend, wie geht es Ihnen?

Addendum

Reaction to a comment:

If someone asks you "Wie geht es dir/Ihnen?" your response should be an answer to this question, not another question! The standard answer is to say "thank you" (for being asked) and then you say, that you're fine. Then you ask the same question. Then it's the first person's task to say "thank you I'm fine".

Two examples:

Walter and Irene meet at the bus station. They are colleagues, working together in the same office (so they use "du" instead of "Sie"), and they live in the south of the german speaking area (so their preferred greeting phrase is "Servus").

Walter: Servus, wie geht's dir?

Irene: Servus, danke gut, und dir?

Walter: Danke, auch gut.

Translation:

Walter: Hello, how are you?

Irene: Hello, thank you, I'm fine, how are you?

Walter: Thank you, I'm fine too.

Frau Müller is owner of a little grocery, Herr Jäger is one of her customers (so they use "Sie", not "du"), and they live in northern regions (so their preferred greeting phrase is "Guten Tag"), and they meet at a bus station too.

Frau Müller: Guten Tag, wie geht es Ihnen?

Herr Jäger: Guten Tag, danke gut, und Ihnen?

Frau Müller: Danke, auch gut.

The translation is the same dialogue as above, just with other names.

In English, asking "What do you do?" is asking what job they have. In German, that would be "Was machen Sie beruflich?" or "Was sind Sie von Beruf?"

You are confusing this with the formal English greeting "How do you do?" As Hubert says, this would translate as "Wie geht es (Ihnen)?"

This meaning of "do" was originally a question about your health, not a more general enquiry about everything in your life. It's worth mentioning that this use of "do" is archaic, and the phrase "How do you do?" has survived past the point where this meaning of the word is still in use. In German, a possible reply to "Wie geht's?" is "Mir geht es gut". In modern English, it is no longer correct to answer "How do you do?" with "I do well", which would have been the natural answer hundreds of years ago. Instead you would reply "I'm well" or "I'm good", because this was a question about your health, and the reply reflects that

Also note that the first "do" is an auxiliary verb, used in the same way as in the sentence "Where do you go after school?" Without the auxiliary verb, the question would be "How do you?" The auxiliary verb is always required for this form of question in modern English (except if the verb in the question is"to be" - "How are you?" for example is fine). In Shakespeare's time the auxiliary verb was not required, so his characters will say "How do you?" or "Where go you?" Most English people will still understand it, but it is incorrect in modern English, and will be recognised either as a sign that the speaker is still learning English, that the speaker is reading from some Middle Ages text, or perhaps that they are telling a joke set in the Middle Ages.

As a further footnote, the equivalent phrase "How's it going?" in English still survives as an informal greeting, and "It's going great" is a perfectly valid reply.