Is "des" not needed after "de"?

Question

In the following sentence:

Tu sais combien de secondes ça fait?

I thought "des" is needed before plural nouns (secondes), so at first I thought the following is correct:

Tu sais combien de des secondes ça fait?

But this is not correct. So my questions are:

• Why is "des" not needed before "de"?

• In what case is it not needed? At first I thought it is not needed before a proposition, but is this correct?

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I got more confused to see the following sentence (use of des, not de):

Tous les mardis et mercredis des deux mois.

In this case, des, not de, is used.

Answer 1

de+des reduces to de. So, combien de+des secondes gives combien de secondes. See the lemma here

http://research.jyu.fi/grfle/053.html

and here

http://www.patenotte.name/Aix/Ecriture/Feuilles_aides_pedagogiques/articles_leur_suppression.html

as well as an English language article

http://www.forum.french-linguistics.co.uk/forum/topics/when-to-use-only-de-instead-of-du-de-la-des

E.g.

Je  voudrais  du  pain->J'ai besoin de pain.

Je voudrais de l'argent->J'ai besoin d'argent (argent is a masculine word starting with a vowel).

But note the difference.

J'ai besoin d'argent (besoin de+de la where de preposition and de la partitive article)

with

J'ai besoin de l'argent que tu me dois.

Here (avoir besoin) de (preposition) + de la (definite article) gives de l' (du argent becomes de l'argent).

Answer 2

I think it is because it is related to quantity. According to the this website:

Example:

When used with nouns, expressions of quantity are always followed by de (d' if the noun begins with a vowel sound).

Tammy et Tex reçoivent des amis ce soir. Tammy est dans la cuisine. Tex regarde la télévision.

Tammy: Une douzaine de crêpes, c'est trop pour quatre personnes?

Tex: Mais non, Tammy, ce n'est pas assez. Il faut préparer beaucoup de crêpes.