I believe it should be correct. Duolingo used “mostrar” very similarly in one of its own sentences. (“La policía mostró tu foto por el museo” or something like that)

I was wondering about that too. I used Mostrar and I am thinking it should be correct.

Very simply, the word show is mostrar. Demostrar is to demonstrate. I'm not sure why they used it here.

“Os” is the reflexive pronoun for “vosotros” (mostly used in Spain) It is odd that Duolingo would give you that as a correction, because Duolingo does not teach “vosotros” as it is not common in Latin America. Sometimes its corrections seem sort of random!

Keep the "te lo" together: Ahora voy a demostrártelo. (Accent mark to keep the stress where it was originally.)
studyspanish.com (Grammar Unit Four)

I put 'les lo voy a demostrar' which I believe also to be a correct answer, but perhaps I should have also put 'a Ustedes' at the end. Os is the familiar plural form of 'you', which is used in Spain, but not in S.America, so I guess it just depends on where you are and how many alternative answers have been programmed in as to whether our answers are accepted or not. If anyone has a helpful comment to make on this it would be gratefully received.

I did the same, but Marcy Brown above writes: Keep the "te lo" together: Ahora voy a demostrártelo. (Accent mark to keep the stress where it was originally.) studyspanish.com (Grammar Unit Four)

Mostraré is “I will show” and voy a mostrar is “I am going to show.” So it is a very similar meaning but not the answer that Duolingo is looking for.

Read the response by LF9zZ earlier in this thread, near the top. He (or she) explains it.

If you are trying to use "le" to refer to "a usted," then it would have to be "Ahora se lo voy a mostrar (a usted)" or "Ahora voy a mostrárselo (a usted)." "Le" and "les" become "se" when they come before the direct object pronouns lo, la, los and las.

You need the indirect object pronoun, to make it "Ahora voy a mostrártelo (a ti)." You are correct, however, that "mostrar" should not be conjugated in this case.

I think you need an indirect object pronoun, "Ahora voy a mostrárselo a usted" is most likely accepted.

Yes, the indirect object or reflexive pronoun always goes before the direct object pronoun.

You have to keep the te lo together. It can be either te lo voy a demostrar or voy a demostrártelo, but you can't separate them apart from each other.