На следующий день мы доели овощи, допили чай из термоса и решили, что такой отдых нам подходит.

На следующий день is a fixed, very common way to say the next day / on the following day.

Here, следующий день is in the accusative case because this expression is idiomatic with на.

• следующий = following / next
• день = day
• на следующий день = the next day

For a learner, the important thing is to remember this as a set phrase. Russian often uses certain prepositions in time expressions in ways that do not match English exactly.

Also, день is masculine and inanimate, so in the singular its accusative form looks the same as the nominative:

• nominative: следующий день
• accusative: следующий день

So even though the form looks unchanged, the case is accusative.

The verbs доели and допили contain the prefix до-, which often gives the meaning of finishing something completely, especially finishing what remained.

So:

• ели = were eating / ate
• доели = finished eating
• пили = were drinking / drank
• допили = finished drinking

In this sentence, доели овощи suggests that the vegetables were already there and they ate the rest of them.
Likewise, допили чай из термоса suggests they finished the remaining tea from the thermos.

This is a very natural use of до- in Russian.

Доели is:

• past tense
• plural
• perfective

In the past tense, Russian verbs agree in gender/number, not person:

• masculine singular: доел
• feminine singular: доела
• neuter singular: доело
• plural: доели

The subject мы tells you that it means we finished eating.

The same applies to допили and решили:

• мы доели
• мы допили
• мы решили

Овощи is the accusative plural form, because it is the direct object of доели.

The dictionary form is:

• singular: овощ
• plural: овощи

For inanimate nouns, the accusative plural is the same as the nominative plural, so:

• nominative plural: овощи
• accusative plural: овощи

That is why the form does not change visibly here.

Из requires the genitive case, so:

• термос = nominative
• из термоса = genitive after из

So чай из термоса means tea from the thermos.

This is a very common pattern:

• вода из бутылки = water from the bottle
• суп из кастрюли = soup from the pot
• чай из термоса = tea from the thermos

A learner should remember: из + genitive.

In Russian, a comma is normally used before что when it introduces a subordinate clause.

Here:

• main clause: мы решили
• subordinate clause: что такой отдых нам подходит

So the structure is:

• We decided, that...

In natural English, we often omit that, but in Russian что is very common and the comma is required.

Решили is perfective because it refers to a completed decision: they came to a conclusion.

• решили = decided
• решали = were deciding / used to decide / tried to decide

In this sentence, the point is the result: after eating and drinking, they reached a conclusion. So решили is the natural choice.

If you said решали, it would sound like the decision process was ongoing, not completed.

Такой means such / this kind of.

So такой отдых means this kind of отдых / this sort of отдых.

Grammatically:

• такой is an adjective-like word
• it agrees with отдых in gender, number, and case

Since отдых is masculine singular, we get:

• такой отдых

The phrase refers back to the kind of rest or vacation experience described in the sentence: simple food, tea from a thermos, outdoor or modest отдых.

Because the verb подходить in the meaning to suit / to be suitable for takes the dative case, not the accusative.

So:

• мы = nominative
• нам = dative
• нас = accusative/genitive

Therefore:

• нам подходит = suits us / is suitable for us
• нас подходит = incorrect in this meaning

This is a very important Russian pattern:

• Мне подходит это время. = This time suits me.
• Тебе подходит этот вариант? = Does this option suit you?
• Нам подходит такой отдых. = This kind of vacation suits us.

Because the verb agrees with the grammatical subject, not with нам.

In the clause:

• такой отдых = subject
• нам = indirect object in the dative
• подходит = verb agreeing with отдых

Since отдых is singular masculine, the verb is singular:

• такой отдых подходит

Even though нам means to us, it does not control the verb form.

Yes. Russian word order is more flexible than English, although this version is natural and neutral.

The original sentence flows well because it presents events in sequence:

1. доели овощи
2. допили чай из термоса
3. решили, что...

You could change the order for emphasis, for example:

• На следующий день мы допили чай из термоса, доели овощи и решили, что такой отдых нам подходит.
• Такой отдых нам подходит, решили мы на следующий день...

But these versions either shift emphasis or sound more literary. The original sentence is the most straightforward and natural for ordinary narration.

It can mean both in different contexts, but here отдых is broader than simple physical rest.

In this sentence, такой отдых most likely means something like:

• this kind of отдых
• this kind of leisure/trip/getaway/vacation style

So it refers not just to relaxing, but to the whole way they are spending time. Russian отдых often covers a wider area than English rest.

Yes, very normal. Russian often lists completed actions this way, especially in narration.

Here the sentence gives a sequence of finished actions:

• they finished the vegetables
• they finished the tea
• they decided something

Because all three verbs are perfective past plural, the sentence feels neat and complete. This is a common storytelling pattern in Russian.