Избранное правление должно отчитаться о работе.

Because it agrees with правление, which is a neuter singular noun in Russian.

• правление = board / governing body / management
• It is grammatically neuter singular
• So any adjective or participle modifying it must also be neuter singular

That is why you get:

• избранное правление = the elected board

Even though a board is made up of several people, Russian treats правление as a single collective noun, so the grammar stays singular.

Here правление means something like:

• board
• governing board
• management body
• committee in charge

A learner may know правление from other contexts where it can also mean rule/reign/government period, but in this sentence, because it is modified by избранное and followed by a duty to report, the meaning is clearly an elected board or governing body.

Должно agrees with правление.

The word должен / должна / должно / должны changes according to the gender and number of the subject:

• он должен
• она должна
• оно должно
• они должны

Since правление is neuter singular, the correct form is должно.

In this structure, должно + infinitive means must / has to / is supposed to:

• правление должно отчитаться = the board must report

Избранное is the full form of a past passive participle used like an adjective.

It comes from the verb избрать = to elect / to choose.

So:

• избранный = elected / chosen
• избранное = neuter singular form

In this sentence it simply describes правление:

• избранное правление = the elected board

For many learners, it is easiest to think of it as an adjective here, even though historically it is a participle.

Because отчитаться is perfective, and here the sentence refers to a single completed act of reporting.

Compare:

• отчитываться = imperfective, to report / to be reporting / to report regularly
• отчитаться = perfective, to give a report / to report back successfully / to account for something

With должно, Russian often uses the perfective infinitive when the focus is on completing the obligation:

• должно отчитаться = must submit/give its report

If the idea were habitual or ongoing, the imperfective might be more likely in a different context.

The -ся is the reflexive ending, but in many verbs it does not translate literally as oneself.

In отчитаться, it is just part of the standard verb meaning:

• отчитаться = to report back / to account for one’s work

So you should learn отчитаться as a whole vocabulary item, not as отчитать + ся in the everyday sense.

For English speakers, the best approach is:

• memorize отчитаться о чём-то
• meaning to report on something

Работе is in the prepositional case because it follows the preposition о.

A very common pattern is:

• о + prepositional = about / concerning

So:

• о работе = about the work

The noun changes like this:

• работа = nominative
• о работе = prepositional

This is a very common Russian pattern:

• говорить о книге = to talk about a book
• думать о семье = to think about family
• отчитаться о работе = to report on the work

It can often be understood as about the work / about its activities / about the work it has done.

Russian often leaves possession unstated when it is obvious from context. In English, you might naturally say:

• report on its work
• report on the work done
• report on its activities

Russian simply says о работе, and the exact English wording depends on context.

Yes. Russian word order is flexible, although the neutral order here is very natural:

• Избранное правление должно отчитаться о работе.

You could rearrange it for emphasis, for example:

• О работе должно отчитаться избранное правление.

That would put more focus on о работе or on who exactly must report.

For a learner, though, the original sentence is the most straightforward and neutral version.

Yes, it sounds fairly formal or official.

Words like:

• правление
• должно
• отчитаться

are very common in administrative, organizational, business, or institutional language.

So this sounds like something you might see in:

• meeting minutes
• official rules
• organizational bylaws
• reports
• announcements

In casual speech, people might choose simpler wording depending on the situation, but this sentence is completely normal in formal Russian.