The correct order of the paragraphs is:
1. D (Greetings from Moscow!...)
2. A (First of all, we are going to do a lot of sightseeing...)
3. C (Mum can't wait to go shopping...)
4. B (I'm going to take lots of interesting pictures...)
Explanation:
* Paragraph D is the most logical opening as it introduces the fact that Lucy has just arrived in Moscow.
* Paragraph A follows naturally as it describes the planned sightseeing activities.
* Paragraph C then introduces the mother's desire to go shopping.
* Paragraph B concludes the letter with a mention of bringing back a Matryoshka.