That's just how it works. Without the article it would mean 'a horse of theirs is beautiful'.
There is short reading material before you enter the exercises. You can access it as well by clicking 'Tips & Notes'. See below.
>When talking about a noun being possessed - we add the word "ה" (the) to the noun. When we are talking to the noun, no "ה" is needed.
I am having trouble identifying שלכם and שלהם when spoken. Could anyone please help me?
When you pronounce שלהם you keep the tongue in the same position during the letters להם. When you pronounce שלכם, you raise the back of the tongue to make a strong the כ sound between ל and ם.