Το κουτί πρώτων βοηθειών είναι δίπλα στον πίνακα οδηγιών.

Because κουτί is a neuter noun in Greek.

Greek nouns have grammatical gender:

• ο = masculine
• η = feminine
• το = neuter

So:

• το κουτί = the box

A useful thing to notice is that many neuter nouns use το in the singular.

It is in the nominative singular, because it is the subject of the sentence.

The structure is:

• Το κουτί πρώτων βοηθειών = the first aid box
• είναι = is
• δίπλα στον πίνακα οδηγιών = next to the instruction board

Since the box is the thing being described, κουτί stays in the nominative.

Είναι is the 3rd person singular form of είμαι (to be), and it works for:

• he is
• she is
• it is

Since το κουτί means it / the box, Greek uses είναι:

• Το κουτί είναι... = The box is...

So yes, it agrees with a singular subject, but Greek does not have separate present-tense forms for he/she/it is the way English uses different pronouns. All three use είναι.

This is a very common type of Greek structure.

πρώτων βοηθειών is in the genitive plural and literally means something like:

• of first aids
• more naturally: of first aid

The full phrase:

• κουτί πρώτων βοηθειών = first aid box

Word by word:

• πρώτων = genitive plural of πρώτος (first)
• βοηθειών = genitive plural of βοήθεια (help, aid)

Greek often uses the genitive to link nouns in expressions like this, where English often uses a noun as an adjective:

• κουτί πρώτων βοηθειών = first aid box
• literally: box of first aid

This is basically a fixed expression.

Because πρώτων βοηθειών is functioning as a descriptive genitive phrase attached to κουτί.

Greek often does this without an article when the second part describes the type or purpose of the first noun:

• κουτί πρώτων βοηθειών = first aid box
• πίνακας οδηγιών = instruction board

If you added an article there, it would usually change the feel or make it sound more specific in a different way. In this sentence, the article is not needed.

Δίπλα means next to / beside.

It is often used with σε:

• δίπλα σε κάτι = next to something

So here:

• δίπλα στον πίνακα = next to the board

You can think of it as:

• δίπλα = beside
• σε + τον πίνακα = at / to the board

Together:

• δίπλα στον πίνακα = beside the board

Because στον is the normal contracted form of:

• σε + τον = στον

This contraction is extremely common in Modern Greek.

Other similar forms:

• σε + τη(ν) = στη(ν)
• σε + το = στο
• σε + τους = στους
• σε + τις = στις
• σε + τα = στα

So:

• δίπλα στον πίνακα = next to the board

This is much more natural than saying δίπλα σε τον πίνακα.

Because after σε (here hidden inside στον), the noun goes in the accusative.

The dictionary form is:

• ο πίνακας = the board / panel / chart

But in the accusative singular:

• τον πίνακα

So:

• στον πίνακα = σε + τον πίνακα

This is why the ending changes from -ας to -α.

Πίνακας is a broad word and can mean different kinds of board, panel, chart, or display depending on context.

In this sentence, πίνακας οδηγιών most naturally means something like:

• instruction board
• instruction panel
• possibly notice board with instructions

So the exact English translation can vary slightly depending on the real-life setting.

Οδηγιών is the genitive plural of οδηγία (instruction).

So:

• οδηγία = instruction
• οδηγίες = instructions
• οδηγιών = of instructions

In the phrase:

• πίνακας οδηγιών

Greek is using a genitive phrase to describe what kind of board it is:

• literally: board of instructions
• naturally: instruction board

This is the same pattern as:

• κουτί πρώτων βοηθειών

Because the main noun is πίνακας, and that noun is definite here:

• στον πίνακα = next to the board

But οδηγιών is just modifying πίνακα as a genitive phrase:

• πίνακας οδηγιών = board of instructions / instruction board

So the article goes with the main noun:

• τον πίνακα

The genitive noun οδηγιών does not need its own article in this kind of expression.

The sentence as written is perfectly normal:

• Το κουτί πρώτων βοηθειών είναι δίπλα στον πίνακα οδηγιών.

But Greek word order is fairly flexible, especially when the meaning is already clear from articles and endings.

Possible alternatives include:

• Δίπλα στον πίνακα οδηγιών είναι το κουτί πρώτων βοηθειών.
• Το κουτί είναι δίπλα στον πίνακα οδηγιών.
  if the context already makes clear which box

Changing the word order can shift the emphasis:

• starting with Δίπλα στον πίνακα οδηγιών emphasizes the location

Yes, absolutely. That is a very useful observation.

Both follow this pattern:

noun + genitive phrase

Examples in this sentence:

• κουτί πρώτων βοηθειών = box of first aid
• πίνακας οδηγιών = board of instructions

This pattern is extremely common in Greek and often corresponds to English compounds or noun modifiers.

A few similar examples:

• ζώνη ασφαλείας = seat belt
  literally belt of safety
• στάση λεωφορείου = bus stop
  literally stop of bus
• οδηγός χρήσης = user guide / guide for use

So this sentence is good practice for recognizing that structure.

A rough pronunciation guide is:

To kou-TI PRO-ton vo-i-THI-on EE-ne DI-pla ston PEE-na-ka o-thi-GHI-on

A few notes:

• κουτί is stressed on the last syllable: κου-ΤΙ
• πρώτων is stressed on πρώ-
• βοηθειών has the stress on the last syllable: βοηθει-ΩΝ
• δίπλα is stressed on δί-
• πίνακα is stressed on πί-
• οδηγιών is stressed on the last syllable: οδηγι-ΩΝ

Also, γ before front vowels often sounds softer than English g.

Greek does not use an indefinite article in the same way English uses a/an.

So:

• Το κουτί πρώτων βοηθειών = the first aid box
• Κουτί πρώτων βοηθειών can mean a first aid box or just first aid box, depending on context

Greek often expresses indefiniteness simply by leaving out the article.

For example:

• Υπάρχει κουτί πρώτων βοηθειών. = There is a first aid box.

So if you want the phrase to be indefinite, you would usually remove το.

It is a general phrase meaning first aid, and it appears in many combinations.

For example:

• κουτί πρώτων βοηθειών = first aid box
• φαρμακείο πρώτων βοηθειών = first aid kit / first aid cabinet
• μαθήματα πρώτων βοηθειών = first aid lessons
• παροχή πρώτων βοηθειών = provision of first aid

So it is useful to learn πρώτες βοήθειες / πρώτων βοηθειών as a set expression.

The nominative form is:

• πρώτες βοήθειες = first aid

But after another noun, Greek often uses:

• πρώτων βοηθειών = of first aid