מזיק או מכרסם יכולים לפגוע בארגז קרטון.

מזיק means pest or harmful creature in a general sense.

מכרסם means rodent more specifically, literally something like a gnawer.

So the sentence is pairing:

• מזיק = a general pest
• מכרסם = a rodent, such as a mouse or rat

A rodent can be a kind of מזיק, but מכרסם is more specific.

This is a very natural question.

Grammatically, יכולים is masculine plural. You might expect יכול instead, because each noun by itself is singular:

• מזיק = singular
• מכרסם = singular

In real Hebrew, when two nouns are linked, speakers sometimes use a plural verb because they are treating them as a combined set of possibilities: a pest or a rodent.

However, many learners will notice that מזיק או מכרסם יכול לפגוע... also sounds very reasonable, especially if the meaning is either one can damage the box.

So:

• יכול would emphasize each possible single agent
• יכולים can sound more general, like talking about these types of creatures as a group

Hebrew often expresses can with the word יכול plus an infinitive.

So:

• יכול = can / is able to
• יכולים = can / are able to
• לפגוע = to harm / to damage

Together, יכולים לפגוע means can damage or more literally are able to damage.

This is different from English, where can is its own modal verb. In Hebrew, יכול behaves more like a regular adjective/participle that changes for gender and number:

• יכול = masculine singular
• יכולה = feminine singular
• יכולים = masculine plural
• יכולות = feminine plural

Because the nouns it refers to are masculine.

Both of these are masculine singular nouns:

• מזיק
• מכרסם

So the matching plural form is יכולים, which is masculine plural.

If the subject were feminine plural, you would use יכולות instead.

Yes — לפגוע has a fairly broad meaning.

Depending on context, it can mean:

• to hurt
• to harm
• to injure
• to damage
• sometimes even to hit/strike

In this sentence, because the object is ארגז קרטון (a cardboard box), the most natural English meaning is to damage.

So the verb is the same, but English changes depending on context:

• לפגוע באדם = to hurt a person
• לפגוע ברכב = to damage a car
• לפגוע בארגז = to damage a box

Because לפגוע normally takes the preposition ב־.

So in Hebrew you say:

• לפגוע ב... = to harm / damage something

That means the thing affected comes with ב־, not with the direct-object marker את.

So:

• לפגוע בארגז = to damage the box / a box

This is just how the verb works in Hebrew. It is one of those verbs whose object is introduced by a preposition.

Not in this sentence.

Normally, ב־ often means in, on, or at, so it is easy to think that בארגז means in a box. But after לפגוע, the ב־ is required by the verb itself.

So here:

• לפגוע בארגז does not mean to harm inside a box
• it means to harm the box

Context tells you which meaning is intended.

In Hebrew, a material or type is often expressed with a noun after another noun.

So:

• ארגז = box / crate / carton
• קרטון = cardboard

Together:

• ארגז קרטון = a cardboard box

English often uses an adjective-like word in this kind of phrase, but Hebrew commonly uses a noun-noun combination.

You can think of it as:

• a box of cardboard
• or more naturally, a cardboard box

Because the sentence is making a general, indefinite statement.

It is not talking about:

• the pest
• the rodent
• the cardboard box

It is talking about any pest, any rodent, and any cardboard box of that kind.

So the nouns are indefinite:

• מזיק = a pest
• מכרסם = a rodent
• ארגז קרטון = a cardboard box

If you added ה־, it would become more specific.

Yes. That would make the subject clearly plural:

• מזיקים = pests
• מכרסמים = rodents

Then יכולים would match very straightforwardly.

That version would feel more like: Pests or rodents can damage a cardboard box.

By contrast, the original sentence uses singular nouns but a plural verb, which gives it a more general or category-based feel.

Many speakers would find that version very natural, yes.

Using יכול makes the agreement singular, which fits the singular nouns more directly:

• מזיק או מכרסם יכול לפגוע בארגז קרטון

That can sound especially natural if you mean: A pest or a rodent can damage a cardboard box.

So the original sentence is understandable, but a learner should know that the singular verb version is also very plausible and may sound more expected in careful grammar.