Η προσαύξηση φαίνεται εδώ.

Η is the feminine singular definite article, so here it means the.

It matches προσαύξηση, which is a feminine singular noun. Greek articles must agree with the noun in gender, number, and case, so η προσαύξηση means the increase / the increment / the surcharge, depending on context.

Also, because it is at the beginning of the sentence, η is capitalized as Η.

Προσαύξηση is feminine.

One clue is the article η, which marks it as feminine singular nominative here. Another clue is the noun ending -ηση, which is very commonly feminine in Greek.

So:

• η προσαύξηση = feminine singular nominative
• this is the subject of the sentence

It is in the nominative case.

In this sentence, η προσαύξηση is the subject, and subjects are normally in the nominative in Greek. The verb φαίνεται agrees with that subject.

So the basic structure is:

• η προσαύξηση = subject
• φαίνεται = verb
• εδώ = adverb of place

Φαίνεται comes from φαίνομαι and literally means something like:

• appears
• is visible
• can be seen
• sometimes seems, depending on context

In this sentence, the most natural idea is appears here or is shown here.

A useful thing to know is that φαίνομαι is very often used where English might use either appear or seem.

That is a very common learner question. Φαίνεται looks like a middle/passive form, and historically it is. But in Modern Greek, φαίνομαι functions as the normal verb for appear / seem / be visible.

So even though it has passive-style endings, you should usually learn it as its own verb:

• φαίνομαι = I appear / I seem
• φαίνεται = he/she/it appears, or it seems

In this sentence, η προσαύξηση φαίνεται εδώ is not best understood as a true passive like is being seen here. It is more naturally the increase appears here or the surcharge is shown here.

Because the subject, η προσαύξηση, is singular.

Greek verbs agree with their subject in person and number. Since προσαύξηση is one thing, the verb is third person singular:

• φαίνομαι = I appear
• φαίνεσαι = you appear
• φαίνεται = he/she/it appears

Here the subject is an it, so φαίνεται is the correct form.

Εδώ is an adverb meaning here.

It tells you the place where something appears or is shown. So it modifies the verb φαίνεται:

• φαίνεται εδώ = appears here / is shown here

It does not change form, because adverbs in Greek do not decline like nouns and articles do.

Yes, you could.

Greek word order is more flexible than English word order. The original sentence, Η προσαύξηση φαίνεται εδώ, is a neutral, straightforward way to say it.

But you can also say:

• Εδώ φαίνεται η προσαύξηση.

This puts more focus on εδώ = here.

In many cases, both are grammatically correct, but the emphasis changes:

• Η προσαύξηση φαίνεται εδώ. = neutral statement
• Εδώ φαίνεται η προσαύξηση. = here is being emphasized

A careful pronunciation is approximately:

pro-SAF-xi-si

A few helpful notes:

• The stress is on -saf-: προσαύξηση
• The letter combination αυ is pronounced af here because the next sound is voiceless
• ξ sounds like ks
• ση sounds like see or si, depending on your accent in English

So a rough English-friendly guide is: pro-SAF-ksee-see

A rough pronunciation is:

FE-ne-te

More exactly:

• stress is on the first syllable: φαίνεται
• αι is pronounced like e
• -ται at the end is also pronounced te in Modern Greek

So: φαίνεται ≈ FE-ne-te

Greek usually does not need subject pronouns unless they are being emphasized.

English says:

• It appears here

Greek normally just uses the verb:

• φαίνεται εδώ

If the subject is stated as a noun, as here, that noun is enough:

• Η προσαύξηση φαίνεται εδώ.

So Greek often leaves out words like he, she, or it when the verb form or the noun already makes the subject clear.

Not naturally in English, even though φαίνεται can also mean seems in other contexts.

With εδώ, the sentence is much more naturally understood as:

• appears here
• is visible here
• is shown here

The meaning seems is more common in structures like:

• Η προσαύξηση φαίνεται μεγάλη. = The increase seems big.

So in your sentence, φαίνεται εδώ is best understood in the visual/display sense, not the opinion/judgment sense.

You generally would not do that in a normal neutral sentence if you mean the increase.

Greek uses the definite article more often than English. So if you are talking about a specific known item, η προσαύξηση is the normal choice.

Without the article, προσαύξηση would sound less natural in this sentence unless you were using a special style, a heading, a label, or a very elliptical note.

So for ordinary sentence use:

• Η προσαύξηση φαίνεται εδώ. = normal

Yes, absolutely.

It has everything needed for a complete statement:

• η προσαύξηση = subject
• φαίνεται = finite verb
• εδώ = adverb giving location

Greek does not require extra words like it is or there is if the verb already expresses the idea clearly. So this is a fully natural complete sentence.