Ana explică astfel problema.

• Ana = Ana (a woman's name)
• explică = explains / is explaining
• astfel = thus, in this way, like this
• problema = the problem

So the sentence means something like Ana explains the problem in this way.

Because problema is the definite form: the problem.

• problemă = a problem
• problema = the problem

In Romanian, the definite article is usually attached to the end of the noun instead of being a separate word like English the.

It is built into problema.

Romanian often puts the definite article at the end of the noun:

• fată = a girl
• fata = the girl
• problemă = a problem
• problema = the problem

So problema already includes the meaning of the problem.

Explică is the 3rd person singular present tense of the verb a explica = to explain.

That means it can translate as:

• he explains
• she explains
• it explains
• or sometimes is explaining, depending on context

Here, because the subject is Ana, it means Ana explains or Ana is explaining.

It can mean either one, depending on context.

Romanian present tense often covers both:

• a general/habitual meaning: Ana explains the problem like this
• a current action: Ana is explaining the problem like this

Without more context, both are possible.

Astfel means in this way, like this, or thus.

In this sentence, it tells you how Ana explains the problem. It is an adverb of manner.

So:

• Ana explică astfel problema = Ana explains the problem in this way

It is a little more formal or written-sounding than everyday așa.

They are similar, but astfel is usually a bit more formal, careful, or literary.

• astfel = thus / in this way
• așa = like this / like that / so

In everyday speech, many speakers would more naturally say something with așa, such as:

• Ana explică problema așa.
• Ana explică așa problema.

But astfel is completely correct and common, especially in more formal speech or writing.

Yes, the word order can change.

Romanian word order is fairly flexible, especially with adverbs. This sentence could also be:

• Ana explică problema astfel.

Both are correct. The difference is mostly one of style, rhythm, or emphasis.

• Ana explică astfel problema can sound a bit more formal or literary.
• Ana explică problema astfel may feel slightly more straightforward to some learners.

In both cases, astfel tells you the manner of explaining.

It is the direct object, so functionally it is in the accusative.

Here, though, the form problema looks the same as the nominative/accusative form of the noun. That is normal in Romanian.

Because problemă is an inanimate noun, you do not use pe before it.
Compare:

• Ana explică problema. = Ana explains the problem.
• Ana vede pe Maria. = Ana sees Maria.

The marker pe is often used with specific human direct objects, but not with something like problema.

Yes, Romanian often drops subject pronouns when the verb already shows the person.

For example:

• Explică astfel problema. = He/She explains the problem in this way.

But in your sentence, Ana is included because the speaker wants to say specifically Ana is the one doing the explaining.

So Romanian can omit subjects, but names and nouns are used when they identify who the subject is.

A simple pronunciation guide is:

AH-na eks-PLEE-kə AST-fel pro-BLE-ma

A few helpful points:

• Ana has stress on the first syllable: AH-na
• explică has stress on -pli-
• ă is pronounced like a short, relaxed uh sound
• astfel has stress on the first syllable: AST-fel
• problema has stress on ble

A rough IPA version is:

/ˈa.na eksˈpli.kə ˈast.fel proˈble.ma/

Yes, it is natural and correct.

It sounds slightly more formal because of astfel, but it is perfectly normal Romanian. A more everyday version might use așa, but your sentence is good Romanian and something you could definitely encounter in speech or writing.