Termino de enjuagar la vajilla y luego guardo la cubertería en el cajón.

Because terminar de + infinitive is the normal structure for to finish doing something.

So here:

• termino = I finish
• de enjuagar = rinsing

Together, termino de enjuagar means I finish rinsing.

A useful warning: this is different from acabo de + infinitive, which means I have just done something. So:

• Termino de enjuagar = I finish rinsing
• Acabo de enjuagar = I’ve just rinsed

Spanish often uses the present tense to talk about:

• habitual actions
• routines
• a sequence of actions being described in a general way

So this sentence can sound like someone describing their usual kitchen routine: first this, then that.

If you wanted to describe one completed event in the past, you would normally use the preterite:

• Terminé de enjuagar la vajilla y luego guardé la cubertería en el cajón.

Because Spanish usually drops subject pronouns when the verb ending already makes the subject clear.

Here, termino and guardo both end in -o, which tells you the subject is I.

So:

• Termino = I finish
• Guardo = I put away / I store

You can add yo if you want emphasis, contrast, or clarity, but it is not necessary in a neutral sentence.

Not exactly.

• lavar = to wash
• enjuagar = to rinse

So enjuagar is usually the step after washing, when you remove soap or residue with water.

That is why termino de enjuagar la vajilla sounds natural in a kitchen context: the washing has already happened, and now the speaker is finishing the rinsing part.

La vajilla is a collective noun. It means the dishes, the tableware, or the crockery as a group.

It is broader than los platos, because platos literally means plates. In everyday English, dishes can include cups, bowls, plates, etc., and vajilla works more like that.

So:

• los platos = literally the plates; sometimes used more loosely in everyday speech
• la vajilla = the dishes/tableware as a set or group

In Spain, vajilla is a very natural word for this kind of context.

La cubertería means the cutlery or the silverware as a set or collection.

Los cubiertos usually refers to the individual pieces:

• forks
• knives
• spoons

So the difference is often:

• cubertería = cutlery collectively
• cubiertos = the actual utensils/items

In real life, both can appear in kitchen contexts, but cubertería sounds especially natural when talking about the whole group being stored away together.

Spanish uses the definite article more often than English does.

Here, la vajilla and la cubertería refer to the specific dishes and cutlery involved in the situation, even though English might simply say the dishes and the cutlery without much thought.

Spanish often keeps the article with nouns like these, especially when referring to familiar household items or whole categories in context.

So the articles are completely normal here.

Yes. In this sentence, luego and después can both work.

• y luego guardo la cubertería...
• y después guardo la cubertería...

Both mean and then / and afterwards I put away the cutlery...

A small extra point:

• luego often means then / later
• después also means afterwards, and it is also used in structures like después de
  • noun/infinitive

For example:

• Después de enjuagar la vajilla, guardo la cubertería.

Because guardar algo en + place is the normal pattern for saying to put/store something in a place.

So:

• guardar la cubertería en el cajón = to put the cutlery away in the drawer

A couple of useful details:

• cajón is masculine, so it takes el
• en + el does not contract in Spanish

Only these two common contractions happen:

• a + el = al
• de + el = del

So en el cajón is correct, not a contraction.

Yes, very naturally.

The verb guardar often means:

• to store
• to put away
• to keep

In a household sentence like this, put away is usually the most natural English match, because the idea is not just moving the cutlery, but returning it to its proper place.

So guardo la cubertería en el cajón is very much the kind of thing English speakers would often translate as I put the cutlery away in the drawer.

You would normally use the preterite for a completed sequence:

• Terminé de enjuagar la vajilla y luego guardé la cubertería en el cajón.

That means the speaker is talking about one finished occasion.

Compare:

• Termino ... y luego guardo ... = present, often routine or general sequence
• Terminé ... y luego guardé ... = past, one completed event

This is a very common contrast in Spanish, and it is worth noticing because both versions are completely natural depending on context.