В моей чашке лежит пакетик чёрного чая, а в её кружке — пакетик зелёного.

Because after в when it means in for a location, Russian normally uses the prepositional case.

So:

• чашка → в чашке
• кружка → в кружке

This is the same location pattern as:

• в доме = in the house
• в книге = in the book
• в комнате = in the room

If there were motion into something, Russian would usually use the accusative instead:

• в чашку = into the cup
• в кружку = into the mug

So here it is в моей чашке and в её кружке because the teabags are already there.

Because мой has to agree with the noun it describes in gender, number, and case.

The noun чашка is:

• feminine
• singular
• here in the prepositional case

So мой becomes моей.

Compare:

• моя чашка = my cup
• в моей чашке = in my cup

This is normal adjective/pronoun agreement in Russian.

As a possessive pronoun meaning her, её is indeclinable in standard Russian. That means it does not change its form for case, gender, or number.

So you get:

• её кружка = her mug
• в её кружке = in her mug
• из её кружки = out of her mug

This is different from мой / твой / наш / ваш, which do change.

Be careful: её can also be the accusative/genitive form of она, but in this sentence it is clearly possessive: her mug.

Both can refer to drinking vessels, but there is a usual distinction:

• чашка = cup
• кружка = mug

A чашка is often thought of as smaller, more delicate, often used with tea or coffee. A кружка is usually larger and sturdier.

In real life, the exact boundary is not always strict, just like cup and mug in English, but that is the basic idea.

Russian often prefers a position verb when talking about where an object is.

• лежать = to lie
• стоять = to stand
• сидеть = to sit
• висеть = to hang

A teabag in a cup is naturally thought of as lying there, so лежит sounds very normal.

So:

• В моей чашке лежит пакетик чёрного чая
  = In my cup there is / lies a bag of black tea.

Could you say есть? Sometimes yes:

• В моей чашке есть пакетик чёрного чая

That means something like There is a bag of black tea in my cup, but it sounds less vivid and less natural in this specific physical-location context.

Could you say находится? Yes, but it is more formal or neutral:

• В моей чашке находится пакетик...

That sounds less everyday.

Because пакетик means a small packet / sachet / teabag, and after words like this Russian usually puts the thing inside in the genitive case.

So the pattern is:

• пакетик чего? = a packet of what?
• чая = of tea

Since чая is genitive singular, the adjective also agrees in the genitive singular:

• чёрный чай = black tea
• чёрного чая = of black tea

So:

• пакетик чёрного чая = a teabag / packet of black tea

The same structure appears with many nouns:

• стакан воды = a glass of water
• чашка кофе = a cup of coffee
• бутылка молока = a bottle of milk

Because Russian often leaves out a noun when it is already obvious from context.

In the first part, we already have чая, so in the second part Russian can omit it:

• пакетик зелёного (чая)

This is very natural. The adjective зелёного is standing in for the whole phrase зелёного чая.

English does something similar sometimes:

• black tea ... green one
• a bag of black tea ... a bag of green tea

Russian just omits the repeated noun more freely here.

The dash shows that something has been left out, usually because it is easy to understand from the first clause.

The full version would be:

• а в её кружке лежит пакетик зелёного

But Russian often omits the repeated verb in the second half:

• а в её кружке — пакетик зелёного

So the dash is standing where the omitted лежит would logically be.

This kind of omission is very common in Russian, especially in paired or contrasted clauses.

А often connects two ideas that are being compared or contrasted.

Here the sentence is setting up a contrast:

• in my cup ... black tea
• in her mug ... green tea

So а is very natural.

It does not always mean a strong but. Often it is more like:

• while
• whereas
• and meanwhile / and as for

If you used и, it would feel more like simple addition:

• In my cup ..., and in her mug ...

But а better highlights the comparison between the two drinks.

Russian word order is more flexible than English, and starting with the location is very common.

By putting В моей чашке first, the sentence sets the scene first:

• In my cup ...
• and in her mug ...

Then it tells what is there.

This word order helps the parallel structure:

• В моей чашке лежит пакетик чёрного чая
• а в её кружке — пакетик зелёного

If you said:

• Пакетик чёрного чая лежит в моей чашке

that is also grammatical, but it puts more focus on the teabag itself rather than on the cup as the location.

So the chosen order is natural and stylistically neat because the sentence is comparing two containers.

Because the grammatical subject is пакетик, which is singular.

Even though the sentence contains several nouns, the thing that лежит is:

• пакетик = one teabag

So:

• пакетик лежит = the teabag lies / is lying

If there were more than one, you would use plural:

• В моей чашке лежат пакетики чая = There are teabags in my cup.