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He has taken a picture.
The picture he has taken become popular

He has his picture taken.
The picture he ...... become popular

Fill in the blanks please. I don’t think I can say something like
“The picture he has it taken become popular” so don’t know what to say. Thanks

Firstly, the second sentence in the first example is not grammatical. It should be

The picture he has taken has become popular.

The picture he has taken is a noun phrase. "he has taken" describes "the picture." has become popular is a verb phrase, where the verb "to become" is in the present perfect tense.

As for the second example, I guess the answer could be

The picture he has taken of himself has become popular.

But this is kind of ambiguous. It sounds like someone else is taking his picture (because of the use of the passive voice in the first sentence), but then the phrasing in this second sentence makes it unclear whether "has" is an auxiliary verb (present perfect tense) or a "regular" transitive verb (as in the first sentence). To avoid this ambiguity, it could be reworded as:

The picture he gets taken of himself has become popular.

since "to get a picture taken" has a similar meaning to "to have a picture taken".

There is some ambiguity between using the helping verb "have" for the perfect tense, and using it as an imperative. Nevertheless, there are certain conventions.

He has taken a picture

means that he took the picture himself.

He has his picture taken

means that someone takes a picture of him. However,

The picture he has taken.

by itself, suggests that he is the one who took the picture. If he asked or paid someone else to take a picture of him, it would be more natural to use the past perfect.

The picture he had taken

This is still somewhat ambiguous, so for clarity you should add more detail to define the subject of the picture:

The picture he had taken of himself became popular

Note that it's became popular, not become popular, as the action happens in the past, relative to the current moment.

The first translation looks like this (note that I am providing the two simplest ways of correcting the issue with become popular):

He has taken a picture.

→ The picture he has taken became popular.

→ The picture he has taken becomes popular.

Given that, the equivalent translation (keeping it as close as possible in terms of equivalent phrasing) would be this:

He has his picture taken.

→ His picture he has had taken became popular.

→ His picture he has had taken becomes popular.

This is because, in the second version, he has had somebody else take his picture. We can't say he has taken it, because he hasn't, so we have to say he has had it taken.

Also, while a picture becomes the picture in the first pair, his picture can remain as it is.

The phrasing isn't entirely natural, but it's still acceptable—and it follows the same pattern of translation.