Тесные ботинки мешают мне долго гулять.

Because it agrees with ботинки, which is plural.

• ботинок = a boot / shoe
• ботинки = boots / shoes

Russian adjectives must match the noun in gender, number, and case. Since ботинки is plural nominative, the adjective also becomes plural nominative:

• тесный ботинок = a tight shoe
• тесные ботинки = tight shoes

Because the subject is plural: тесные ботинки.

In the present tense, Russian verbs agree with the subject in number (and in the past tense also gender).

• ботинок мешает = the shoe interferes / gets in the way
• ботинки мешают = the shoes interfere / get in the way

So мешают is the correct 3rd person plural form of мешать.

Because мешать normally takes the person affected in the dative case.

So the pattern is:

• что-то мешает кому-то делать что-то
• literally: something hinders to someone doing something
• natural English: something prevents someone from doing something / makes it hard for someone to do something

Examples:

• Мне мешает шум. = The noise is bothering me / preventing me from doing things.
• Тесные ботинки мешают мне долго гулять. = Tight shoes make it hard for me to walk for a long time.

Here:

• я = I
• меня = me (accusative/genitive)
• мне = to me / for me (dative)

With мешать, you usually need мне.

Here мешать means to hinder, to interfere with, to prevent, or to make something difficult.

It does not mean a complete impossibility every time. Often it just means something gets in the way.

So this sentence suggests:

• the shoes are uncomfortable,
• and because of that, walking for a long time is difficult.

Common structure:

• мешать кому-то = to bother/interfere with someone
• мешать кому-то делать что-то = to prevent someone from doing something / make it hard for someone to do something

Because after мешать кому-то you can use an infinitive to say what action is being hindered.

So:

• мешают мне гулять = hinder me from walking
• мешают мне долго гулять = hinder me from walking for a long time

This is very common in Russian:

• Музыка мешает мне работать. = The music prevents me from working / makes it hard for me to work.
• Дождь мешает нам гулять. = The rain prevents us from going for a walk.

Because гулять usually means to walk for pleasure, to go for a walk, or to spend time walking around.

That fits this sentence well: the idea is not just moving from one place to another, but walking around for a while.

Compare:

• гулять = stroll, go for a walk, walk around
• ходить = go on foot, walk in general, go somewhere habitually or repeatedly

So:

• долго гулять = walk around for a long time / go for a long walk
• долго ходить would sound more like walking for a long time in a more general sense, often less natural here

Долго means for a long time.

In Russian, adverbs often come before the infinitive they modify, so:

• долго гулять = to walk for a long time

That is the most natural word order here.

You may also see different word orders in Russian for emphasis, but долго гулять is the neutral, standard version.

Ботинки is in the nominative plural, because it is the subject of the sentence.

You can tell because it is the thing doing the action of мешают:

• Тесные ботинки мешают...
• The tight shoes interfere...

The adjective тесные is also nominative plural to match it.

Russian could use a different structure, but this sentence focuses on the cause of the difficulty, not directly on ability.

Compare:

• Я не могу долго гулять из-за тесных ботинок.
  = I can’t walk for a long time because of tight shoes.

• Тесные ботинки мешают мне долго гулять.
  = Tight shoes prevent me from walking for a long time / make it hard for me to walk for a long time.

The second version is slightly more centered on the shoes as the problem.

In dictionaries, ботинки often means boots or ankle boots, but in real usage it can sometimes be translated more loosely depending on context.

A learner should know:

• ботинок = boot / shoe-like boot
• ботинки = boots

But in some English translations, people may choose shoes if the exact footwear type is not important and the main point is simply that the footwear is too tight.

So the Russian word itself is still ботинки, but the English translation may vary a little.

Yes, Russian word order is flexible, but different orders change the focus or emphasis.

Neutral order:

• Тесные ботинки мешают мне долго гулять.

Possible variations:

• Мне мешают долго гулять тесные ботинки.
• Долго гулять мне мешают тесные ботинки.

These all mean roughly the same thing, but the neutral textbook version is the original one. It sounds natural and straightforward.

Yes, мешать is imperfective.

That makes sense because the sentence describes a general ongoing situation: tight shoes are the kind of thing that interferes with long walks.

In the present tense, Russian uses only the imperfective for ordinary present meaning.

So:

• мешают = are interfering / interfere / hinder

A perfective verb would not be used here for a normal present-tense meaning.

Yes. Мешать can cover both:

• practical interference: something makes an action difficult
• bothering/annoyance: something disturbs or gets in your way

In this sentence, the most likely meaning is practical physical interference: the shoes are too tight, so long walks are difficult. But the verb itself is broad enough that it often carries the general idea of being in the way.