Tanween

بيت الملك الكبيرِ
بيت الملك كبيرٌ
Two seemingly identical sentences but depending on where I put tanween there can be formed two different sentences : the king's GREAT house or the GREAT king's house.

How do You guess the meaning intended since you dont put fatha kesra damma?
Thank You

Zakhid: It's exactly as Ahmad explained, and I want to add that this is how you say:

1. The king's great house: بيت الملك كبيرٌ: you are giving the adj 'great' to the house here,

as in "The king's house is great". ٌكبير is being used with no article, therefore it took tanween.

2. The great king's house: ِبيت الملك الكبير: while in here the adj 'great' is given to the king

himself, as in "This is the house of the great king".

You wrote it wrong, it should be:

بيت الملك الكبير

The sentence has nothing to do with tanween, and it can never have tanween in either word, because tanween never applies to a definite word (if the noun begins with "الـ" it's a definite noun, it can never get tanween).

When the words have no "tashkeel" (vowel marks َ  ِ  ُ  ) we know the meaning through the context, as native speakers, we never really depend on vowel marks, I can know what it should be, and pronounce it correctly without them being written, but it would be more difficult for a non-native, so try to use the vowel marks so you wouldn't be confused.

tanween

Hello Friend. 

Great could mean الكبير او الهائل 

also it means العظيم 

So if you say بيت الملك العظيم 

then you are saying the Great king's house 

and if you say بيت الملك الكبير 
then you are talking about the House. 

the king's great house. 

we use العظيم to describe people often , it is also used to describe objects or events. 

but in this way people will understand you. 

The king's great house = بيت الملك كبير

The great king's house.= بيت الملك الكبير/ العظيم