Learn German: Siehst du den dünnen Anzug?

This is because of how adjectives change after definite articles. Since Anzug is masculine and in the accusative (direct object) case, the article is den. After den, the adjective must take the -en ending. That is why dünn (thin) becomes dünnen.

Why do we use den instead of der Anzug?

The verb sehen (to see) requires a direct object, which takes the accusative case. Since Anzug is a masculine noun (der Anzug), its article changes from der to den when it is the object being seen.

Why does the sentence start with the verb Siehst?

In German, yes/no questions always start with the conjugated verb. Instead of saying 'You see' (Du siehst), you swap the subject and the verb to ask 'Do you see?' (Siehst du). German doesn't use a helper word like 'Do' for questions.

Is the noun Anzug related to the verb anziehen (to put on clothes)?

Yes, it is! German often builds nouns out of verbs. Der Anzug is related to the separable verb anziehen (to put on). So a suit is literally something you put on.