После работы я отвезу бабушку в поликлинику и куплю ей лекарство.

Because после requires the genitive case.

• работа = work (dictionary form, nominative)
• работы = genitive singular

So:

• после работы = after work

This is a very common pattern:

• после урока = after the lesson
• после фильма = after the film
• после обеда = after lunch

Отвезу is the simple future form of a perfective verb.

In Russian, perfective verbs form the future with one word:

• отвезти → я отвезу = I will take / I will drive
• купить → я куплю = I will buy

This is different from imperfective verbs, which usually make the future with быть:

• я буду везти = I will be taking / carrying
• я буду покупать = I will be buying

Here, the speaker is talking about completed actions, so perfective is used:

• first I’ll take Grandma to the clinic
• then I’ll buy medicine for her

This is a very common question.

• повезу focuses on setting off / taking someone somewhere
• отвезу often emphasizes taking someone to a destination, successfully getting them there

In many everyday contexts, both can be translated as I’ll take. But in this sentence, отвезу fits well because the destination is clear:

• в поликлинику = to the clinic

So я отвезу бабушку в поликлинику suggests I’ll take Grandma to the clinic and get her there.

Because it is the direct object of отвезу.

The verb отвезти takes a direct object: the person or thing being taken. For feminine nouns ending in -а, the accusative singular usually changes to -у:

• бабушка (nominative) = grandmother
• бабушку (accusative) = grandmother, as the object

So:

• я отвезу бабушку = I will take Grandma

This is a normal accusative pattern for animate feminine nouns.

Because this sentence expresses motion toward a place, not location in a place.

With в:

• в + accusative = into / to
• в + prepositional = in / inside

So:

• в поликлинику = to the clinic
• в поликлинике = in the clinic

Compare:

• Я иду в школу. = I’m going to school.
• Я в школе. = I’m at school.

Here the speaker is taking Grandma to the clinic, so accusative is required:

• поликлиника → в поликлинику

Because ей means to her / for her, and Russian often uses the dative case for the person who receives something or benefits from the action.

• она = she
• её = her
• ей = to her / for her

In this sentence:

• куплю ей лекарство = I’ll buy her some medicine / I’ll buy medicine for her

Here:

• ей = indirect object, in the dative
• лекарство = direct object, in the accusative (though it looks like nominative because it is neuter inanimate)

Because лекарство is a neuter inanimate noun, and in the singular its accusative form is the same as its nominative form.

• nominative: лекарство
• accusative: лекарство

So although it looks unchanged, it is still functioning as the direct object of куплю.

This happens with many neuter inanimate nouns:

• письмо → я читаю письмо
• окно → я вижу окно

It can mean either, depending on context and tone.

• grandmother is a more neutral dictionary-style translation
• grandma often sounds more natural in everyday English

In Russian, бабушка is very commonly used in normal family speech and often feels warm and natural, much like grandma.

So this sentence could naturally be understood as:

• After work, I’ll take Grandma to the clinic and buy her some medicine.

Not exactly.

A поликлиника is usually an outpatient clinic or medical clinic, not a hospital where people stay overnight.

In many Russian-speaking contexts, a поликлиника is the place you go for:

• appointments with doctors
• checkups
• tests
• prescriptions

So translating it as clinic is usually best. Sometimes medical clinic or outpatient clinic gives a more precise sense.

Because the speaker is describing two completed future actions.

• отвезу = I will take
• куплю = I will buy

Russian often uses perfective future when talking about a sequence of things someone will do. It sounds natural and definite:

• После работы я отвезу бабушку в поликлинику и куплю ей лекарство.

This means something like:

1. after work, I’ll take Grandma to the clinic
2. and I’ll buy medicine for her

The actions are presented as whole, completed events.

Yes, Russian word order is fairly flexible, but the original order is neutral and natural.

Original:

• После работы я отвезу бабушку в поликлинику и куплю ей лекарство.

This sounds like a normal statement: first the time expression, then the subject, then the actions.

You could rearrange parts for emphasis, for example:

• Я после работы отвезу бабушку в поликлинику и куплю ей лекарство.
• Бабушку я после работы отвезу в поликлинику и куплю ей лекарство.

But these may shift emphasis slightly. For learners, the original sentence is a very good standard model.

It can cover several English possibilities depending on context:

• medicine
• medication
• a medicine
• a drug (less common as a basic translation in everyday family contexts)

In this sentence, лекарство most naturally means medicine or some medicine.

So:

• куплю ей лекарство = I’ll buy her some medicine

English often prefers some medicine here even though Russian does not use a separate word for some.

Russian often does not need an article or a separate word like some where English does.

So:

• куплю ей лекарство literally looks like I will buy her medicine
• but in natural English it is often I’ll buy her some medicine

Russian has no articles (a, the) and often leaves this kind of quantity/generalness unstated unless it needs to be specific.

It could be omitted, because the verb endings already show the subject:

• отвезу
• куплю

Both clearly indicate I.

So Russian could also say:

• После работы отвезу бабушку в поликлинику и куплю ей лекарство.

That is perfectly natural in context. Including я can make the subject a little clearer or slightly more emphatic, but it is not always necessary.

A useful breakdown is:

• После работы = after work
• я = I
• отвезу бабушку в поликлинику = will take Grandma to the clinic
• и = and
• куплю ей лекарство = will buy her some medicine

So the structure is:

time expression + subject + future action 1 + and + future action 2

This is a very common Russian sentence pattern for talking about planned actions.