Después de responder, podemos pasar a otra pregunta.

Because después is followed by de before an infinitive.

A very common pattern in Spanish is:

• después de + infinitive
• antes de + infinitive

So:

• Después de responder = After answering
• Antes de salir = Before leaving

You cannot normally say después responder in standard Spanish.

After después de, Spanish normally uses the infinitive when the action is general or when no new subject is introduced.

So:

• Después de responder, ... literally means After answering, ...

This is similar to English after answering rather than after I answer.

If you wanted to make the subject more explicit with a full clause, you would need a different structure, for example:

• Después de que respondamos, ... = After we answer, ...

But in your sentence, the infinitive is the natural and simple option.

The comma separates the introductory phrase from the main clause:

• Después de responder, = introductory time phrase
• podemos pasar a otra pregunta = main clause

In English, we often do the same:

• After answering, we can move on to another question.

In Spanish, this comma is very natural here because the opening phrase sets the scene before the main idea.

Podemos means we can. It adds the idea of possibility or permission:

• podemos pasar = we can move on
• pasamos = we move on / we are moving on

Using podemos sounds a little softer and more natural in this context, especially in conversation or teaching. It suggests:

• Now that we’ve answered, we can go on
• not a hard command, just the next possible step

Because Spanish usually omits subject pronouns when the verb already makes the subject clear.

• podemos already means we can
• so nosotros podemos is usually unnecessary

Spanish uses subject pronouns mainly for emphasis, contrast, or clarity.

Compare:

• Podemos pasar a otra pregunta. = normal, neutral
• Nosotros podemos pasar a otra pregunta. = more emphatic, like we can move on

Here, pasar a means to move on to or to go on to.

So:

• pasar a otra pregunta = move on to another question

This is a very common expression in Spanish, especially in lessons, presentations, meetings, and interviews.

Examples:

• Vamos a pasar al siguiente tema. = We’re going to move on to the next topic.
• Pasemos a la siguiente pregunta. = Let’s move on to the next question.

Because the verb phrase is pasar a algo — to move on to something.

The a belongs to the verb structure:

• pasar a otra pregunta
• pasar al siguiente punto
• pasar a la práctica

So the a does not mean a person is receiving the action; it is simply required by pasar a in this meaning.

In Spanish, otro / otra usually works by itself and does not normally combine with un / una.

So you say:

• otra pregunta = another question

Not:

• una otra pregunta

This is different from English, where another historically comes from an other, but in modern Spanish the correct form is simply otra.

Because pregunta is a feminine noun in Spanish:

• la pregunta
• therefore: otra pregunta

The adjective or determiner must agree with the noun:

• otro libro
• otra pregunta
• otros temas
• otras respuestas

So otra matches pregunta in gender and number.

Yes, and it changes the nuance slightly.

• otra pregunta = another question
• la siguiente pregunta = the next question

Both are correct, but they are not identical:

• otra pregunta just means one more question, a different one
• la siguiente pregunta points more clearly to the next item in order

In a classroom or quiz context, both would sound natural.

This sentence is completely standard and natural across the Spanish-speaking world, including Spain.

Nothing in it is especially regional. All of these are very widely understood and used:

• después de + infinitive
• podemos
• pasar a otra pregunta

So this is good general Spanish, not just Spain-specific Spanish.