Отсюда до библиотеки можно дойти пешком за десять минут.

Отсюда means from here.

• здесь = here (location)
• отсюда = from here (starting point)

So in this sentence, отсюда tells you where the walk starts.

Examples:

• Я здесь. = I am here.
• Я иду отсюда домой. = I am going home from here.

After до, Russian uses the genitive case. The preposition до means to, up to, or as far as in the sense of reaching a point.

So:

• библиотека = library
• до библиотеки = to the library

This is a very common pattern:

• до дома = to the house / home
• до станции = to the station
• до магазина = to the store

Because it is in the genitive singular after до.

The dictionary form is:

• библиотека

Its genitive singular form is:

• библиотеки

This happens because many feminine nouns ending in -а change to -и or -ы in the genitive singular.

Compare:

• школа → до школы
• комната → до комнаты
• библиотека → до библиотеки

Можно means something like it is possible, one can, or you can.

In this sentence, можно дойти means:

• it is possible to get there
• you can get there

Russian often uses можно + infinitive without a subject.

Examples:

• Можно войти? = May I come in? / Is it possible to come in?
• Здесь можно курить? = Is it allowed to smoke here?
• До станции можно доехать на автобусе. = You can get to the station by bus.

So the sentence does not literally say you, but English usually translates it with you can.

Дойти means to reach on foot, to walk as far as, or to get to a place by walking.

This sentence is about successfully reaching the library, so дойти fits well.

Useful comparison:

• идти = to be going, to walk in one direction
• ходить = to go/walk regularly or in general, or there and back
• дойти = to get there on foot, to make it there by walking

Examples:

• Я иду в библиотеку. = I am going to the library.
• Я хожу в библиотеку каждый день. = I go to the library every day.
• Я дошёл до библиотеки. = I got to the library on foot.

In your sentence, можно дойти пешком means you can get to the library on foot.

Russian often uses a perfective infinitive after можно when talking about the possibility of achieving a result.

Here the result is reaching the library.

So:

• можно дойти = it is possible to get there / to reach it on foot

If you used идти, it would focus more on the process of walking rather than arriving. But this sentence is about the fact that the destination is reachable, so дойти is natural.

Пешком means on foot.

It is a fixed adverbial form used to describe the means of travel:

• идти пешком = to go on foot
• дойти пешком = to get there on foot

For learners, it is easiest to remember пешком as a whole expression rather than trying to build it from scratch each time.

Compare:

• на автобусе = by bus
• на машине = by car
• пешком = on foot

За десять минут means in ten minutes.

With expressions of time, за + accusative often means the amount of time needed to complete something.

So:

• дойти за десять минут = to get there in ten minutes
• прочитать книгу за два дня = to read a book in two days
• сделать работу за час = to do the work in an hour

This is different from:

• десять минут = ten minutes
• через десять минут = in ten minutes from now
• за десять минут = within a span of ten minutes / taking ten minutes

Because after the numeral десять, the noun usually appears in the genitive plural.

So:

• минута = minute
• десять минут = ten minutes

Compare:

• одна минута
• две / три / четыре минуты
• пять минут
• десять минут
• двадцать минут

This is a very important Russian number pattern.

Yes. Russian does not need to say you here.

Можно дойти пешком за десять минут literally means something like:

• It is possible to get there on foot in ten minutes

But in natural English, we usually say:

• You can walk there in ten minutes
• You can get to the library on foot in ten minutes from here

So the subject is general and unspecified, similar to English you in general statements.

Yes, Russian word order is flexible.

The original order:

• Отсюда до библиотеки можно дойти пешком за десять минут.

This is natural because it starts with the starting point from here, then the destination to the library, then the main statement.

Other possible orders could be:

• До библиотеки отсюда можно дойти пешком за десять минут.
• Пешком отсюда до библиотеки можно дойти за десять минут.

These versions are still understandable, but the emphasis changes slightly.

The original sentence sounds neutral and informative.

Yes, absolutely. That is a very natural English translation.

A few good translations are:

• You can walk to the library from here in ten minutes.
• It takes ten minutes to walk to the library from here.
• The library is a ten-minute walk from here.

They are not word-for-word identical, but they express the same idea naturally in English.

A neutral pronunciation would usually stress the most informative parts:

Отсю́да до библиоте́ки мо́жно дойти́ пешко́м за де́сять мину́т.

Approximate stress:

• отсю́да
• библиоте́ки
• мо́жно
• дойти́
• пешко́м
• де́сять
• мину́т

A speaker might emphasize different words depending on context:

• Отсюда if contrasting with another starting point
• пешком if contrasting with going by car or bus
• за десять минут if the time is the important part