Новая грамматическая тема: местоимения с частицей «-либо» чаще встречаются в более официальной речи.

Because тема is a feminine noun in Russian, so the adjectives that describe it must also be feminine singular:

• новая = new, feminine singular
• грамматическая = grammatical, feminine singular
• тема = topic, feminine singular

So all three words agree in gender, number, and case.

The colon introduces the content of the new grammar topic.

So the sentence is structured like this:

• Новая грамматическая тема: = New grammar topic:
• местоимения с частицей -либо чаще встречаются в более официальной речи = the explanation of that topic

This is very natural in Russian, especially in teaching materials, headings, or notes.

-либо is a particle added to pronouns and similar words to form indefinite meanings such as some..., any..., or some kind of..., often in a formal or bookish style.

Common examples:

• кто-либо = someone / anyone
• что-либо = something / anything
• какой-либо = some kind of / any
• где-либо = somewhere / anywhere

In this sentence, местоимения с частицей -либо means pronouns formed with this particle.

Местоимения is nominative plural here, because it is the subject of the verb встречаются.

The core of the clause is:

• местоимения ... встречаются = pronouns ... occur / are found

Since местоимения is plural, the verb is also plural.

It is plural because the subject местоимения is plural.

Also, yes, встречаться often means to meet or to date, but here it has a different common meaning: to occur, to appear, or to be found.

So in this sentence:

• чаще встречаются = are more often found / occur more often

That is a very common use in grammar explanations and formal writing.

Чаще means more often.

It is the comparative form related to часто = often.

So:

• часто = often
• чаще = more often

In this sentence, it tells you about frequency: pronouns with -либо are found more often in formal speech.

Here в means in, and it is followed by the prepositional case because it refers to the sphere or context where something occurs.

So:

• в речи = in speech
• в официальной речи = in formal speech
• в более официальной речи = in more formal speech

Речи is the prepositional singular form of речь.

A useful point: Russian uses более + adjective when the adjective directly modifies a noun in a phrase like this. You cannot say в официальнее речи.

Because официальнее is the comparative form, but it does not work as a regular agreeing adjective before a noun.

Russian often uses this pattern when a comparative directly describes a noun:

• более официальный стиль = a more formal style
• в более официальной речи = in more formal speech

So более + adjective is the normal choice here.

Not necessarily only spoken language.

In grammar and style discussions, речь can mean:

• speech
• language use
• register
• style of expression

So в более официальной речи is best understood as in more formal language/register, not only literal spoken speech.

Most often, question-word bases can take it, especially pronouns and pronominal adverbs. For example:

• кто-либо = anyone / someone
• что-либо = anything / something
• какой-либо = any / some kind of
• чей-либо = someone’s / anyone’s
• где-либо = anywhere / somewhere
• когда-либо = ever / sometime
• как-либо = somehow / in any way

So it is not limited to just кто and что.

This is one of the most important questions.

A very simple practical comparison:

• кто-то = someone; a specific person exists, but you do not identify them
• кто-нибудь = someone / anyone; neutral, very common in everyday speech
• кто-либо = someone / anyone; more formal, bookish, or official

Examples:

• Кто-то звонил. = Someone called.
• Позови кого-нибудь. = Call someone.
• Если у вас возникнут какие-либо вопросы... = If you have any questions...

So in many contexts, -либо is close in meaning to -нибудь, but it sounds more formal.

Yes. In standard Russian spelling, -либо is written with a hyphen:

• кто-либо
• что-либо
• какой-либо

The same is true for similar particles such as -то and -нибудь:

• кто-то
• кто-нибудь

So you should not write them as one solid word or as separate words.

Yes, you can, and it will be understood. But it often sounds more formal, official, or written than everyday neutral speech.

For everyday conversation, speakers more often use -нибудь or -то:

• everyday: У тебя есть какие-нибудь вопросы?
• more formal: Есть ли у вас какие-либо вопросы?

So the sentence is teaching you a style point: -либо is correct, but it is especially common in formal language.