Я забыл закрыть кавычки и потом долго не мог понять, где заканчивается предложение.

Because забыть + infinitive often means to forget to do something.

Here, закрыть is perfective, so it refers to one complete action: to close the quotation marks.

• Я забыл закрыть кавычки = I forgot to close the quotation marks.
• Я забывал закрывать кавычки would suggest a repeated/habitual problem: I used to forget to close quotation marks.

So in this sentence, the speaker means one specific forgotten action, which is why закрыть is the natural choice.

Кавычки means quotation marks.

In Russian, this word is normally used in the plural, because quotation marks come as a pair:

• открыть кавычки = to open quotation marks
• закрыть кавычки = to close quotation marks

So even if English sometimes says a quotation mark or the closing quote, Russian usually just uses the plural кавычки for the punctuation marks as a set.

It is in the accusative, but for inanimate plural nouns, the accusative often looks exactly like the nominative.

So:

• nominative: кавычки
• accusative: кавычки

Since закрыть takes a direct object, кавычки is in the accusative here, even though the form does not visibly change.

Yes, it is natural.

It literally means to close the quotation marks, and it is exactly what you would say if someone forgot to type the closing quotation mark(s).

Russian commonly talks about punctuation this way:

• открыть скобку = open a bracket/parenthesis
• закрыть скобку = close a bracket/parenthesis
• открыть кавычки = open quotation marks
• закрыть кавычки = close quotation marks

Because не мог понять emphasizes difficulty over a period of time.

• не понял = did not understand
• не мог понять = could not understand / could not figure out

Since the sentence also includes долго (for a long time), не мог понять fits very well:

• потом долго не мог понять = then for a long time I couldn’t figure out...

This gives the idea that the speaker struggled for a while, not just that understanding failed once.

Because понять is perfective and means to come to understanding, to figure out, to grasp.

After мочь, Russian often uses:

• imperfective infinitive for general ability or process
• perfective infinitive for managing to achieve a result

Here the intended idea is result-based: the speaker could not figure out where the sentence ended.

So:

• не мог понять = couldn’t figure out
• не мог понимать would sound more like couldn’t understand in a general ongoing sense, which is less natural here

Because in Russian, an indirect question like где заканчивается предложение often uses the present tense to describe a fact being identified: where the sentence ends.

The speaker is not talking about a future event. They are trying to locate the endpoint of the sentence in the text.

So this works like English:

• I couldn’t understand where the sentence ends

Even though English often prefers ended in this context, Russian very naturally uses present tense here because it expresses the sentence’s boundary as a current textual fact.

Because где заканчивается предложение is a subordinate clause.

More specifically, it is an indirect question after понять:

• не мог понять, где заканчивается предложение
• literally: couldn’t understand where the sentence ends

Russian normally separates this kind of subordinate clause with a comma.

Предложение is in the nominative case.

That is because it is the subject of заканчивается:

• предложение заканчивается = the sentence ends

So inside the clause где заканчивается предложение, the word предложение is the thing doing the action of ending.

Because Russian often omits a repeated subject when it is already clear.

The sentence begins with Я забыл..., and after that the second part is understood to have the same subject:

• Я забыл... и потом долго не мог понять...

Russian does not need to repeat я unless there is a special reason, such as emphasis or contrast.

So this is completely natural and stylistically normal.

Потом means then, afterward, or later.

It shows the sequence of events:

1. Я забыл закрыть кавычки
2. и потом долго не мог понять...

So the meaning is:

• first, I forgot to close the quotation marks
• then, as a result, I spent a long time unable to figure out where the sentence ended

Without потом, the sentence would still make sense, but потом makes the timeline clearer.

Yes, that is also possible.

Both verbs can mean to end:

• кончаться
• заканчиваться

In many contexts they are interchangeable. Here:

• где заканчивается предложение sounds neutral and standard
• где кончается предложение is also understandable and natural, though заканчиваться may sound a little more formal or bookish in this context

So the version in your sentence is a very good standard choice.

It has two main parts joined by и, and the second part contains a subordinate clause.

Structure:

• Я забыл закрыть кавычки
• и потом долго не мог понять, где заканчивается предложение

So:

1. Main clause: Я забыл закрыть кавычки
2. Main clause: потом долго не мог понять
3. Subordinate clause attached to понять: где заканчивается предложение

This is a very common Russian pattern:

• [main clause] + [verb of knowing/understanding] + comma + [indirect question]

For example:

• Я не знаю, где он живёт.
• Она не поняла, почему он ушёл.

Your sentence follows that same pattern.