Хоть бы этот кочан капусты и редис остались свежими до вечера.

Хоть бы expresses a strong wish or hope, often with a hint of worry, impatience, or desperation.

In English, it is often close to:

• if only ...
• I just hope ...
• please let ...

So this is not a neutral statement. It sounds emotional: the speaker is hoping the cabbage and radishes will still be fresh by evening.

You will often see the same pattern in sentences like:

• Хоть бы дождь прекратился. — If only the rain would stop.
• Хоть бы он позвонил. — I just wish he’d call.

This is a very common Russian pattern.

After бы, Russian uses the past-tense form of the verb to express:

• wishes
• hypotheticals
• conditionals
• unreal situations

So остались here does not mean real past time. It is part of a wish construction.

Compare:

• Они остались — They stayed / remained (real past)
• Хоть бы они остались — If only they would stay / remain (wish)

So the form looks past, but the meaning is not past here.

Because the subject is a compound subject:

• этот кочан капусты
• и редис

These two things are joined by и, so the verb agrees with them in the plural.

That is why we get:

• остались — plural
• свежими — also plural

Even though редис looks singular, the whole subject refers to more than one item overall, so plural agreement is natural.

Because after verbs like быть, стать, оказаться, остаться, Russian often uses the instrumental case for a predicate noun or adjective.

Here свежими means fresh as the state they remain in.

So:

• остаться свежим / свежей / свежими = to remain fresh

This is the normal pattern.

Why plural instrumental?

• свежими is plural because the subject is plural in meaning.
• It is instrumental because it is the complement after остались.

A learner often wants nominative here, but with остаться, the instrumental is the standard choice.

Because этот agrees with кочан, not with капуста.

The phrase is:

• кочан капусты = a head of cabbage

The main noun, or head noun, is кочан, which is:

• masculine
• singular

So the demonstrative must match кочан:

• этот кочан

The word капусты is dependent on кочан and does not control the agreement here.

Russian often uses a container/unit noun + genitive structure.

So:

• кочан капусты = literally a head of cabbage
• бутылка воды = a bottle of water
• кусок хлеба = a piece of bread

Here кочан is the unit noun, and капусты is in the genitive to mean of cabbage.

So this is not possession. It is the normal way Russian says what kind of head it is.

Grammatically, редис is a singular masculine noun.

But in food and shopping contexts, it can be used in a more collective / substance-like way, similar to talking about the vegetable in general rather than one single radish. So in English it may be translated as radishes depending on context.

If you want to emphasize individual radishes, Russian may use:

• редиски — plural count form

So here редис is perfectly natural, even though English may prefer a plural translation.

Because the preposition до always takes the genitive case.

So:

• до вечера = until evening
• до утра = until morning
• до понедельника = until Monday

This is just the normal case pattern after до.

Because и is simply joining two coordinated parts of the subject:

• этот кочан капусты
• редис

When Russian has a single и connecting two homogeneous elements, it normally does not use a comma.

So the punctuation here is standard.

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

The sentence begins with Хоть бы, which is very common because it immediately sets the emotional tone: if only / I just hope.

Then the subject comes:

• этот кочан капусты и редис

Then the verb and predicate:

• остались свежими

And finally the time limit:

• до вечера

You could rearrange parts for emphasis, but the original version sounds normal and clear. The main thing that should stay intact is the relationship between:

• хоть бы
  • wish construction
• the compound subject
• остались свежими as the predicate idea