Learn Russian: Они хотят безопасно пройти через парк. - They want to pass through the park safely.

The prefix про- focuses on moving through or past a space, which makes sense for walking through a park. The prefix пере- implies crossing over an obstacle or moving from one distinct side to another, like crossing a street (перейти улицу) or a bridge.

Why is пройти followed by через парк? What case is парк in?

When talking about going through a space, the verb пройти is commonly paired with the preposition через (through). Через always takes the accusative case. Because парк is an inanimate masculine noun, its accusative form looks exactly the same as its dictionary form.

After хотят (they want), why do we use the perfective verb пройти instead of the imperfective проходить?

We use the perfective пройти because they want to successfully complete the action of passing through the park on this one specific occasion. If they were talking about a desire to make a regular habit of walking through the park, they would use the imperfective проходить.

Why does безопасно end in -о?

It is an adverb, which often end in -о in Russian. It is formed from the adjective безопасный (safe). Because it describes how the action (пройти) is done rather than describing a noun, we must use the adverb form.