После промаха он взял новый дротик.

Because после requires the genitive case.

• Dictionary form: промах
• Genitive singular: промаха

So:

• после промаха = after the miss

This is a very common pattern in Russian:

• после урока = after the lesson
• после работы = after work
• после дождя = after the rain

So the form промаха is there because of the preposition после.

Промах is a noun meaning a miss, a failed shot/throw, or more generally a mistake in some contexts.

In this sentence, because of дротик (dart), it most naturally means a miss in throwing/shooting at a target.

It is related in meaning to the verb промахнуться = to miss.

So the sentence uses a noun:

• После промаха... = After the miss...

rather than a verb-based structure like After he missed...

Взял is the past tense of взять, which is a perfective verb meaning to take.

Here it shows a completed single action:

• he took a new dart

That fits the context well: first there was a miss, then he took another/new dart.

Compare:

• взял = took, completed action
• брал = was taking / used to take / took repeatedly, depending on context

In this sentence, взял is the natural choice because it describes one specific next step in the sequence of events.

That is how Russian forms the past tense for many verbs.

For past tense, Russian also shows gender in the singular:

• он взял = he took
• она взяла = she took
• оно взяло = it took
• они взяли = they took

So взял is masculine singular because the subject is он.

It is the direct object, so it is in the accusative case. But for masculine inanimate nouns, the accusative often looks exactly like the nominative.

So:

• nominative: новый дротик
• accusative: новый дротик

They are the same in form here.

This happens because:

• дротик is masculine
• дротик is inanimate

If it were animate, the accusative would often look different. For example:

• nominative: новый студент
• accusative: нового студента

But with дротик, there is no visible change.

Дротик means dart, the small pointed object thrown in the game of darts.

It is a masculine noun.

Its basic forms are:

• nominative singular: дротик
• genitive singular: дротика
• plural: дротики

In this sentence, it is the direct object of взял.

Yes, Russian often can omit pronouns when the subject is clear from context.

So Взял новый дротик can be possible in the right situation, especially in narration where the subject is already obvious.

But он is included here to make the subject explicit:

• После промаха он взял новый дротик.

This can sound more natural if:

• the subject has just been introduced
• there could be confusion about who did the action
• the speaker wants a bit of emphasis or clarity

So он is not strange at all, even though Russian does not need subject pronouns as often as English does.

Yes. Russian word order is flexible, though not random.

This sentence:

• После промаха он взял новый дротик.

is a very natural way to present the sequence:

1. after the miss
2. he took a new dart

Other orders are possible, for example:

• Он взял новый дротик после промаха.

This still means basically the same thing, but it sounds a little different in focus. The original version foregrounds the time/background first: after the miss.

Russian often puts time or context at the beginning of the sentence, especially in narration.

Yes, in English that can be a very natural translation, even though the Russian structure is literally after the miss.

Russian is using a noun phrase:

• после промаха = literally after the miss

But English often prefers a verbal idea:

• after missing
• after he missed

So the Russian and English structures do not have to match word-for-word.

Literally, новый means new.

In context, English might sometimes say another dart, especially if the idea is simply that he picked up the next one. But the Russian word here is still новый, not другой.

Useful comparison:

• новый дротик = a new dart
• другой дротик = a different/another dart
• ещё один дротик = one more dart / another dart

So if the sentence specifically says новый дротик, the basic meaning is a new dart.

The stress is:

• После → по́сле
• промаха → прома́ха
• он → он
• взял → взял
• новый → но́вый
• дротик → дро́тик

So the full sentence is pronounced roughly:

По́сле прома́ха он взял но́вый дро́тик.

A couple of useful notes:

• In взял, the вз cluster can feel difficult at first.
• г is not in this sentence, but х in промаха is the normal Russian kh sound, as in Bach or loch for many learners.

Russian has no articles.

So Russian does not have separate words for a and the. Whether something is definite or indefinite is understood from:

• context
• word order
• intonation
• the situation itself

So новый дротик could be understood in English as:

• a new dart
• the new dart

depending on context, though a new dart is the most natural default here.