Το χαρτοκιβώτιο είναι άδειο.

Το is the definite article, meaning the. It is the neuter singular form of the article, used because χαρτοκιβώτιο is a neuter singular noun.

So:

• το χαρτοκιβώτιο = the cardboard box

If you wanted a cardboard box, you would normally say ένα χαρτοκιβώτιο.

Yes. Greek often makes long compound words, and χαρτοκιβώτιο is one of them.

It is built from elements related to:

• χαρτί = paper
• κιβώτιο = box / case / carton

So the word means something like cardboard box / carton. It is more specific than just κουτί, which is a more general word for box.

There are two clues here:

1. It takes the article το, which is the neuter singular article.
2. It ends in -ο, which is a very common ending for neuter nouns in Greek.

So in this sentence, το χαρτοκιβώτιο is a neuter singular subject.

Είναι is the present-tense form of είμαι, meaning to be. Here it means is.

A useful thing to know is that είναι is used for both:

• he/she/it is
• they are

So:

• Το χαρτοκιβώτιο είναι άδειο. = The cardboard box is empty.
• Τα χαρτοκιβώτια είναι άδεια. = The cardboard boxes are empty.

In both sentences, the verb is είναι.

Because Greek adjectives must agree with the noun they describe in gender, number, and case.

Since χαρτοκιβώτιο is neuter singular, the adjective also has to be neuter singular:

• άδειος = masculine
• άδεια = feminine
• άδειο = neuter

So:

• Το χαρτοκιβώτιο είναι άδειο. is correct because both the noun and adjective are neuter singular.

Because Greek does not need a separate subject pronoun here. English often uses it, but Greek can simply use the noun itself as the subject:

• Το χαρτοκιβώτιο = the subject
• είναι άδειο = is empty

So Greek does not need an extra word equivalent to it in this sentence.

Because άδειο is a predicate adjective after the verb είναι. In Greek, just like in English, you normally do not put an article before an adjective in this position.

So:

• Το χαρτοκιβώτιο είναι άδειο. = The cardboard box is empty.

Not:

• Το χαρτοκιβώτιο είναι το άδειο unless you mean something different, such as the empty one in a contrastive context.

The most neutral and natural order here is:

• subject + verb + adjective
• Το χαρτοκιβώτιο είναι άδειο.

Greek word order is more flexible than English, so other orders are possible for emphasis, but this version is the standard one for a simple statement.

For example, Άδειο είναι το χαρτοκιβώτιο could be used for emphasis, but it is less neutral.

Roughly:

• har-to-ki-VO-tee-o

A few pronunciation notes:

• The stress falls on βώ.
• The first letter χ is not like English h. It is a harsher sound, like the ch in Scottish loch or German Bach.
• κι sounds like kee.
• τιο at the end is pronounced clearly; the word has several syllables.

So try something like: khar-to-ki-VO-ti-o.

Roughly:

• A-thi-o

More accurately:

• the stress is on the first syllable: Α
• δ here sounds like the th in this
• ει is pronounced like ee
• the ending -ο is a separate vowel sound

So άδειο is approximately AH-dhee-o.

The accent marks show which syllable is stressed.

In this sentence:

• χαρτοκιβώτιο → stress on βώ
• είναι → stress on εί
• άδειο → stress on ά

Greek accent marks are very important because they tell you where to place the stress when speaking.

Yes, but the meaning changes slightly.

• Το χαρτοκιβώτιο είναι άδειο. = The cardboard box is empty.
  This refers to a specific box.
• Ένα χαρτοκιβώτιο είναι άδειο. = A cardboard box is empty.
  This refers to a non-specific box.

So both are grammatical, but το and ένα do not mean the same thing.