Dia bilang tidak usah sungkan; kalau butuh apa-apa, saya boleh mengetuk pintunya kapan saja.

Because the sentence is reporting what someone said to the speaker.

• Dia bilang = He/She said
• saya boleh mengetuk pintunya = I may/can knock on his/her door

So the person being talked about is dia, while saya is the speaker/narrator. This is very normal in Indonesian reported speech.

Tidak usah means no need to, you don’t have to, or don’t bother.

So tidak usah sungkan is literally something like no need to feel hesitant/awkward, but in natural English it often means don’t hesitate.

Not exactly.

• jangan = don’t / a direct prohibition
• tidak usah = no need to / you don’t have to

So tidak usah sungkan sounds softer and more reassuring than jangan sungkan, though both can be heard. In hospitality contexts, tidak usah sungkan is very natural.

Sungkan is a very common Indonesian word, but it does not match one single English word perfectly.

It can mean feeling:

• hesitant
• awkward
• reluctant
• too polite to impose
• shy in a social/polite way

So tidak usah sungkan is a common friendly expression meaning something like:

• please don’t hesitate
• don’t feel awkward
• make yourself comfortable asking

Because Indonesian often leaves out a subject when it is already clear from context.

Here, kalau butuh apa-apa literally means if [someone] needs anything. From the next clause, saya boleh mengetuk pintunya, we understand that the omitted subject is saya.

So the meaning is:

• if I need anything

This kind of omission is very common in natural Indonesian.

Here apa-apa means anything.

So:

• butuh apa-apa = need anything

This is not a literal what-what translation. In Indonesian, apa-apa often appears in contexts like negatives, questions, and conditionals to mean anything or something at all.

For example:

• Ada apa-apa? = Is something wrong?
• Tidak ada apa-apa. = Nothing is wrong / There’s nothing.

Because boleh is about permission, while bisa is usually about ability.

• boleh = may, be allowed to
• bisa = can, be able to

In this sentence, the speaker is saying that the person gave them permission to knock on the door. So boleh is the best fit.

Ketuk is the base word meaning knock or tap.
Mengetuk is the active verb form with the meN- prefix.

This is a standard Indonesian pattern:

• base: ketuk
• active verb: mengetuk

Because the root starts with k, that k drops after meN-, so you get mengetuk, not mengketuk.

In more casual speech, people may sometimes say ketuk without the prefix, but mengetuk is the standard form here.

Pintunya means his/her door here.

• pintu = door
• -nya = his/her/its, or sometimes the, depending on context

In this sentence, -nya most naturally refers back to dia, so:

• mengetuk pintunya = knock on his/her door

A useful thing to remember is that -nya is very flexible in Indonesian. It can mark possession, or it can make something definite.

Kapan saja means anytime or whenever.

• kapan = when
• saja adds a sense of any / freely / no restriction

So kapan saja means that any time is fine.

Because Indonesian often leaves out bahwa (that) after verbs like bilang or mengatakan, especially in everyday language.

So:

• Dia bilang tidak usah sungkan...
  = He/She said (that) there was no need to hesitate...

Adding bahwa is possible, but it usually sounds a bit more explicit or formal:

• Dia bilang bahwa tidak usah sungkan...

Both are grammatical, but omitting bahwa is very common.