Learn Hardcore Portuguese (Portugal): Eles tentam manter um relacionamento saudável mesmo quando estão ocupados. - They try to maintain a healthy relationship even when they are busy.

In Portuguese, the subject pronoun (eu, tu, ele, ela, nós, vocês, eles, elas) is often optional, because the verb ending usually shows who the subject is.

Eles tentam manter… = They try to keep… (explicit subject)
Tentam manter… = (They) try to keep… (subject understood from -am ending)

You use Eles mainly:

when you want to emphasise who is doing the action,
or when the context is not clear and you might confuse eles with vocês, elas, etc.

So both Eles tentam manter… and Tentam manter… are correct in European Portuguese.

What exactly is tentam? Which tense and person is it, and what does it imply?

Tentam is:

verb: tentar (to try)
tense: present indicative
person/number: 3rd person plural (they / vocês)

A mini present-tense conjugation of tentar:

eu tento – I try
tu tentas – you try (informal singular)
ele / ela tenta – he/she tries
nós tentamos – we try
vocês tentam – you (plural) try
eles / elas tentam – they try

In this sentence, the present tense describes a habitual action: something they try to do regularly, not just right now.

Why is it tentar manter and not something like tentar de manter or tentar a manter?

In Portuguese, tentar is followed directly by the infinitive, with no preposition:

tentar fazer – to try to do
tentar manter – to try to keep
tentar entender – to try to understand

So you say:

Eles tentam manter um relacionamento saudável…

and not:

✗ Eles tentam de manter…
✗ Eles tentam a manter…

Those forms are incorrect here. Just tentar + infinitive.

Why is it manter and not manterem? When do we use that -em ending on infinitives?

Manter is the normal infinitive (to keep).
Manterem is a personal infinitive (inflected infinitive), used mainly after prepositions when you want to mark who the subject is:

Depois de eles manterem um relacionamento saudável…
After they keep / having kept a healthy relationship…

In your sentence, tentar already controls the subject:

Eles tentam manter…

The subject of manter is the same as the subject of tentam (eles), and tentar takes the plain infinitive, so you use manter, not manterem.

Using Eles tentam manterem… is non‑standard/wrong in this context in European Portuguese.

What’s the difference between um relacionamento saudável and uma relação saudável? Which is more natural in Portugal?

Both are correct, but there are some nuances and preferences:

um relacionamento saudável
- very common in both Portugal and Brazil;
- often used for romantic or close interpersonal relationships;
- slightly more specific and “psychological” in feel.
uma relação saudável
- also common, especially in European Portuguese;
- broader meaning: relation / connection, not only romantic (e.g. uma relação saudável com os colegas – a healthy relationship with colleagues).

In European Portuguese:

For a romantic couple, both um relacionamento saudável and uma relação saudável sound natural.
Relação is perhaps a bit more general and frequent in everyday speech, but relacionamento is absolutely normal and not marked.

Why do we say um relacionamento and not o relacionamento here?

The choice between um (a) and o (the) is about definiteness:

um relacionamento saudável
- a healthy relationship, in general;
- we are not talking about one specific, previously identified relationship;
- it sounds more general: They try to keep a healthy relationship (as a quality).
o relacionamento saudável
- the healthy relationship;
- refers to a specific, already known relationship;
- would usually sound odd here unless the relationship had already been clearly identified earlier in the conversation.

In your sentence, we’re describing the quality of their relationship, so um relacionamento saudável is the natural choice.

Why is saudável singular, but ocupados is plural? Shouldn’t they both be plural?

They agree with different words:

um relacionamento saudável
- noun: relacionamento (singular, masculine)
- adjective: saudável (singular, matches relacionamento)
eles estão ocupados
- subject pronoun: eles (plural, masculine or mixed group)
- adjective: ocupados (plural, matches eles)

So:

saudável agrees with relacionamento (one relationship → singular).
ocupados agrees with eles (they → plural).

If you changed the nouns/pronouns, the adjectives would follow:

relacionamentos saudáveis – healthy relationships
elas estão ocupadas – they (women) are busy

What does mesmo quando mean exactly? Is it the same as mesmo que?

Mesmo quando here means even when:

…um relacionamento saudável mesmo quando estão ocupados.
…a healthy relationship even when they are busy.

Compare:

quando = when
mesmo quando = even when (adds the idea of contrast or difficulty)

Mesmo que is different; it usually means even if / even though, and is followed by a subjunctive:

Mesmo que estejam ocupados, eles tentam manter um relacionamento saudável.
Even if / even though they are busy, they try to keep a healthy relationship.

So:

mesmo quando
- indicative (estão) = even when (factual situations).
mesmo que
- subjunctive (estejam) = even if / even though (more hypothetical or concessive).

Why is it estão ocupados and not são ocupados?

Portuguese distinguishes ser and estar:

estar – temporary states, conditions, locations:
- Eles estão ocupados. – They are busy (right now / during this period).
ser – permanent or defining characteristics:
- Eles são ocupados. – They are busy people (by nature; their lifestyle).

In your sentence, the focus is on moments or periods when they are busy, not on describing them as inherently “busy people”, so estão ocupados is the correct and natural choice.

Why is ocupados masculine plural? What changes if the group is only women?

Ocupados agrees with eles:

eles = they (all male or mixed group) → ocupados
elas = they (all female) → ocupadas

So:

Eles estão ocupados. – They (men / mixed) are busy.
Elas estão ocupadas. – They (women) are busy.

General rule for adjectives:

masculine singular: ocupado
feminine singular: ocupada
masculine (or mixed) plural: ocupados
feminine plural: ocupadas

If you rewrote the whole sentence for a group of women:

Elas tentam manter um relacionamento saudável mesmo quando estão ocupadas.

Can I put Mesmo quando estão ocupados at the beginning of the sentence?

Yes. Both word orders are correct:

Eles tentam manter um relacionamento saudável mesmo quando estão ocupados.
Mesmo quando estão ocupados, eles tentam manter um relacionamento saudável.

Placing Mesmo quando estão ocupados first slightly emphasises the contrast (despite being busy) but the meaning remains the same. This kind of reordering is common and natural in European Portuguese.

Could I drop mesmo and just say quando estão ocupados?

You can, but the nuance changes:

…quando estão ocupados. – when they are busy (neutral: simply at those times)
…mesmo quando estão ocupados. – even when they are busy (adds the idea that this is harder or more surprising)

Without mesmo, you just state when it happens.
With mesmo, you highlight that they make an effort in spite of being busy.

Is this sentence the same in European and Brazilian Portuguese?

Grammatically and lexically, the sentence works in both varieties:

Eles tentam manter um relacionamento saudável mesmo quando estão ocupados.

Differences are mainly:

Pronunciation (European vs Brazilian accent).
Register / preferences: in Portugal, some speakers might also say uma relação saudável, but um relacionamento saudável is still perfectly natural.

So you can safely use this exact sentence in European Portuguese.