A villanyszámla és a gázszámla mutatja az energiafogyasztást.

A quick breakdown:

• A = the
• villanyszámla = electricity bill
• és = and
• a gázszámla = the gas bill
• mutatja = shows
• az = the
• energiafogyasztást = energy consumption as the direct object

So the structure is basically:

the electricity bill and the gas bill show the energy consumption

Because Hungarian very often makes compound nouns.

• villany = electricity / electric power

• számla = bill, invoice
  → villanyszámla = electricity bill

• gáz = gas
• számla = bill
  → gázszámla = gas bill

This is extremely normal in Hungarian. English often writes these as two words, but Hungarian commonly joins them into one.

Hungarian usually repeats the definite article with each coordinated noun when both are definite.

So:

• a villanyszámla és a gázszámla = the electricity bill and the gas bill

This is more natural than leaving the second article out.

Also:

• a is used before a consonant sound
• az is used before a vowel sound

So:

• a villanyszámla
• a gázszámla
• az energiafogyasztás

When energiafogyasztás gets the accusative ending -t, it becomes energiafogyasztást, but the article stays az because the word still begins with a vowel sound.

Mutatja comes from the verb mutat, meaning to show.

The -ja ending tells you that the verb is in the definite conjugation:

• mutat = shows something indefinite / shows in general
• mutatja = shows a specific thing

Here the object is specific and definite:

• az energiafogyasztást = the energy consumption

So Hungarian uses the definite form:

• mutatja

This is a very important Hungarian pattern: the form of the verb can change depending on whether the direct object is definite.

The -t marks the direct object in Hungarian. This is the accusative case.

Base noun:

• energiafogyasztás = energy consumption

Direct object form:

• energiafogyasztást = energy consumption, as the thing being shown

So in this sentence, the bills are the subject, and energiafogyasztást is what they show.

A very literal grammatical reading is:

• The electricity bill and the gas bill show the energy-consumption-ACC

Because Hungarian normally does not need subject pronouns when the subject is already clear.

In English, you need:

• It shows
• They show

In Hungarian, the verb ending already helps show the grammatical person/number, and here the subject nouns are stated anyway:

• A villanyszámla és a gázszámla ...

So there is no need to add a separate pronoun.

This is a very good question, and many learners notice it.

With a subject like:

• a villanyszámla és a gázszámla

standard Hungarian would very often use a plural verb:

• A villanyszámla és a gázszámla mutatják az energiafogyasztást.

That is probably the form many teachers and grammars would recommend.

So why might you see mutatja?

• sometimes speakers treat two items as a kind of combined unit
• sometimes real usage is looser than textbook rules
• agreement with coordinated subjects can vary more in actual speech than in strict grammar

But for a learner, the safest choice here is:

• mutatják = show with a plural subject

So this sentence may feel a little unusual as written.

No. Hungarian word order is fairly flexible, but different orders can change what is being emphasized.

This version is a straightforward, neutral order:

• A villanyszámla és a gázszámla mutatja / mutatják az energiafogyasztást.

You could also say:

• Az energiafogyasztást a villanyszámla és a gázszámla mutatja / mutatják.

That puts more attention on az energiafogyasztást.

Because Hungarian marks grammatical roles with articles, verb forms, and case endings, word order can move around more than in English. But the neutral learner-friendly order is often:

subject + verb + object

Yes. Számla can mean bill or invoice, depending on context.

So:

• villanyszámla = electricity bill
• gázszámla = gas bill

In this sentence, the idea is that the bill/document contains information showing the amount of energy used. So the sentence is talking about what you can see on the bill.