Until you get the hang of it, come up with something that helps, like remember:
Ents chu ldi gung
Ents chew oldie gunk
Ents = the tree things in LOTR
chew = but these Ents are from China so they spell it "Chu" because the last name of one of the Ents is Chu.
oldie = The oldest one lost both his arms so chop off the o and e from oldie = ldi
gunk = gung is pronounced like gunk. The "g" and the end of a word is pronounced like "k". You should know this, but for now just remember to spell gunk like gung because you're so gung-ho to learn how to spell Entschuldigung.
Ents chew oldie gunk.
Edit: Please don't use this for the pronunciation!
I think they mean pronunciation. If you know how to pronounce it as en - chul - di- gung, and you know that the English "ch" sound is spelled tsch in German, then as long as you know that you pronounce it with an English ch, then you'll know to spell it tsch. That's how I'm remembering, at least.
It might have made more sense to you if you had been presented with the phrase "ein Entschuldigung ist gut" before this…
If you just say "Entschuldigung" to somebody, it means "my apologies", "I'm sorry", or "forgive me". If you have "die Entschuldigung" it means "the apology", "the excuse".
I got a little bit lucky with this one. It was only the 2nd question with "Entschuldigung" in this lesson and lucky for me I thought to really examine the word before typing the English translation. So that's how I was able to spell it right. I forgot about the noun capitalization thing though!