Thomas a honte des opinions de certains hommes

Question

Thomas a honte des opinions de certains hommes ... why is 'des' used in this case, but 'de' in this case ... Ils ont honte de leurs notes.

Most examples use de or d' ... but 'du' in Nous avons honte du projet final.

Maarten Kamp · Accepted Answer

Brenda,  
“ Thomas a honte des opinions de certains hommes “ - des is the obligatory contraction of the preposition de from the expression ‘ avoir honte de … ‘, and the definite article ‘ les ‘ from ‘ de les ( opinions ) ‘, giving the construct  ‘ des ( opinions ) ‘. 
There is no such contraction between ‘ de ‘ and ‘ leurs ‘ in “ Ils ont honte de leurs notes. “  as the latter is not a definite article and the contraction rules do not apply.
The sentence with ‘ Nous avons honte du projet final. ‘ likewise - ‘ du ‘ is the obligatory contraction of ‘ de le …’. 
From the lesson 
Note that de + le, la, l', les (= of the) follows the contraction rule of de: du, de la, de l', des.  
https://progress.lawlessfrench.com/revision/glossary/article-type/french-articles-contract-in-some-instances 
https://progress.lawlessfrench.com/revision/grammar/contractions-of-articles-a-le-au-a-les-aux-de-le-du-de-les-des

Brenda Spencer · Answer

Thank you Maarten.A very helpful explanation.