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Theory:

And the rain – it has fallen almost daily. Of course, it collects right in our trenches, where we must bail it out with pots and pans. And with the rain has come mud – a good foot or deeper. It splatters and cakes everything, and constantly sucks at our boots. One new recruit got his feet stuck in it, and then his hands too when he tried to get out.
 
Through all this, we could not help feeling curious about the German soldiers across the way. After all, they faced the same dangers we did and slogged about in the same muck. What’s more, their first trench was only fifty yards from ours. Between us lay No Man’s Land, bordered on both sides by barbed wire - yet they were close enough we sometimes heard their voices.

Of course, we hated them when they killed our friends. But other times, we joked about them and almost felt we had something in common. And now it seems they felt the same.
Explanation:
 
The British soldier went on to say that the rain was also a cause of worry for them because it came down every day. Even though the trenches were made for hiding, the rain falls right into the trenches. When the water gets into it, they pour it out using the pots and pans. When the rain falls, it carries the mud along with it into the pit. As a result, the soldier’s feet became muddy and filthy. Mud is strewn throughout their boots and uniforms. Then he said that a new team member’s feet and hands became stuck inside the mud pit when he attempted to come out.
 
Wet_and_muddy_trench_(4687876853).jpg
Muddy trench*

After overcoming all of the challenges, the British soldier stated that they had to focus on the enemy team at all times, even whether they were in the mud or rain. On the other hand, he said that the Germans were going through the same difficulties. They were in the trenches as well, and their trenches were also filled with water and mud. He also stated that their first trench was about 50 yards (50 meters) away from the German soldiers. Then he said that there lay “No Man’s Land” between the German and British team. The term “No Man’s Land” refers to an area or strip of land that no one owns or controls. Also, the place was surrounded by wire fences. However, the enemies were close to them; they could occasionally hear their voices.
 
AWM_E00961_-_no_mans_land_prior_to_attack.jpg
No man's land* (only for reference)
 
The British soldier then said that they hated the German soldiers when they killed their friends. They joked about them at other times, and it almost felt like they shared something in common. While thinking about them, he felt that they also had the same sentiment.
 
Meanings of the difficult words:
 
S.No
Words
Meanings
1
MuckWet, sticky mud or dirt
2
PanAny of various types of metal containers, usually not deep, used for cooking food
3
Splatter Drops of a thick liquid that have splashed or fallen somewhere
4
CakeA thick or sticky substance that hardens when dry and becomes overspread on the surface of an object
5
SuckVery bad or unpleasant
6
BootA type of shoe that covers the whole foot and the lower part of the leg
7
Slog Work hard over a period of time
Reference:
State Council of Educational Research and Training (2018). Term-1 English Standard-9. The Christmas Truce- Aaron Shepard (pp. 126-131). Published by the Tamil Nadu Textbook and Educational Services Corporation.