После работы мне хочется приготовить лёгкий ужин.

Because после requires the genitive case.

• работа = nominative
• работы = genitive singular

So:

• после работы = after work

This is a fixed grammar pattern:

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

So in this sentence, работы is in the genitive because it follows после.

Хочется is a different way to express wanting. It is often less direct and more like:

• I feel like...
• I’d like to...
• I’m in the mood to...

The person who experiences this feeling goes in the dative case, so:

• мне хочется = I feel like / I want
• literally something like to me, it is desired

Compare:

• Я хочу приготовить ужин. = I want to cook dinner.
  More direct and straightforward.
• Мне хочется приготовить ужин. = I feel like cooking dinner.
  More emotional, softer, more spontaneous.

So мне is used because хочется takes the experiencer in the dative.

Yes, but it works a bit differently from хотеть.

Хочется is a common impersonal form related to хотеться, which expresses a desire or urge. It is very often used with a dative pronoun:

• мне хочется
• тебе хочется
• ему хочется

Examples:

• Мне хочется спать. = I feel sleepy / I feel like sleeping.
• Ей хочется кофе. = She wants coffee.
• Нам хочется отдохнуть. = We feel like resting.

So in your sentence:

• мне хочется приготовить... = I feel like cooking...

This construction is extremely common in everyday Russian.

Because хочется is followed by the action someone feels like doing, and that action is usually expressed with the infinitive.

So the structure is:

• мне хочется + infinitive

Examples:

• Мне хочется поесть. = I feel like eating.
• Мне хочется поспать. = I feel like sleeping.
• Мне хочется приготовить ужин. = I feel like cooking dinner.

This works very much like English want to do or feel like doing.

This is about aspect.

• готовить = imperfective
• приготовить = perfective

In this sentence, приготовить suggests completing the action: to prepare / to cook up a dinner.

So:

• Мне хочется приготовить лёгкий ужин. = I feel like making a light dinner.
  Focus on the completed result.

If you used готовить, it would sound more like the process in a general sense, and in this sentence Russian normally prefers приготовить.

A simple way to think of it:

• готовить = to be cooking / to cook in general
• приготовить = to cook / prepare something successfully, as a finished action

Because лёгкий is an adjective agreeing with ужин.

Ужин is:

• masculine
• singular
• in the accusative case here

But since ужин is inanimate, the masculine accusative looks like the nominative. So:

• nominative: лёгкий ужин
• accusative: лёгкий ужин

The adjective must match the noun in gender, number, and case:

• лёгкий = masculine singular
• ужин = masculine singular

So they go together as лёгкий ужин.

Because it is the direct object of приготовить.

You are preparing what?
→ ужин

That makes ужин the direct object, so Russian uses the accusative case.

For masculine inanimate nouns, accusative is the same as nominative:

• nominative: ужин
• accusative: ужин

So the form does not change, even though the case has changed.

Here it means light in the sense of not heavy, easy to digest.

So лёгкий ужин means:

• a light dinner
• not a big, heavy meal

Russian лёгкий can mean several things depending on context:

• лёгкая сумка = a light bag
• лёгкая задача = an easy task
• лёгкий ужин = a light dinner

So context tells you which meaning is intended.

Yes. Russian word order is flexible, although the neutral order here is very natural:

• После работы мне хочется приготовить лёгкий ужин.

Other orders are possible, for example:

• Мне после работы хочется приготовить лёгкий ужин.
• Лёгкий ужин мне хочется приготовить после работы.

But these may shift the emphasis.

The original sentence sounds neutral and natural because it starts with the time expression после работы, then gives the experiencer мне, then the desire хочется, and finally the action.

So while the words can move, the original order is a good standard model to learn.

Yes, absolutely. That sentence is correct.

The difference is mainly in tone:

• я хочу приготовить... = I want to cook...
• мне хочется приготовить... = I feel like cooking...

The first is more direct and definite.
The second is softer and more about mood or inclination.

So both are correct, but they are not identical in feeling.

Because работа here means work as an activity or your job, not separate pieces of work.

So:

• после работы = after work / after finishing work

Russian usually uses the singular for this idea, just as English often does in after work.

Plural работы can exist in other contexts, but here the singular meaning is the normal one.

It looks strange because it contains the particle-like ending -ся, and the spelling does not perfectly reflect how casual speech may sound.

A careful pronunciation is roughly:

• хо́чется

In normal speech, learners often hear something close to:

• ХО-чет-ца

That is because -ться / -тся combinations are often pronounced more simply than they look.

Also note the stress:

• хо́чется
• лёгкий
• ужин
• рабо́ты

Stress matters a lot in Russian, so it is useful to learn each word together with its stress.

Yes. It works very naturally on its own and means:

• after work
• after I finish work
• when work is over

Russian often uses short time expressions like this without adding extra words:

• после урока = after class
• после обеда = after lunch
• после работы = after work

So this phrase is fully natural and does not need anything extra.