I don’t get the game, but you could have done Trier -> tried?
well sure, but Trier is a german city, thus i referenced a german word 
i’ll pass the next word to another user, go ahead 
beer -> bear
Replace 1 letter, +0.
bear -> care
Replaces one letter, swaps the rest around a bit.
+0
care -> tare
Replaces one letter.
+0
tare -> mare
Replaces one letter.
+0
mare -> more
Replaces one letter.
+0
more -> lore
Replaces one letter.
+0
lore -> sore
Replaces one letter.
+0
sore -> core
Replaces one letter.
+0
core -> fore
Replaces the first letter.
+0
fore -> fare
Replaces one letter.
+0
fare -> farm
changes one letter
farm -> karma
replaces one letter and adds one letter
(now I just want to see what my ‘karma’ leads to ;))
karma -> Kara Common English name. Removes one letter, +0.
Kara -> Katara A character’s name from the TV show Avatar: The Last Airbender.
Adds 2 letters.
+2
Katara -> katana
Changes one letter.
+2
Katana -> Banana
Changes 2 letters.
+2
Banana -> Ban
Remove 3 last letters
-1
ban -> man
Changes 1 letter.
-1
man -> mango
Adds 2 letters
+1