Where do the adjective go?

des enfants (jeune)
Is it "des jeunes enfants"??

un quartier et une rue (ancien)
un ancien quartier et une ancienne rue??

Salut! Because of the preceding plural adjective, the tendency is to say "de jeunes enfants" but it precedes the noun.

For the 2nd one, exactly as you wrote it.

Position of Adjectives.

Unlike English adjectives, most descriptive adjectives in French FOLLOW the noun they modify.

une porte secrète = a secret door
les vins blancs = the white wines.

Some short descriptive adjectives that usually PRECEDE the noun are:

beau, bon, court, gentil, grand, gros, jeune, joli, long, mauvais, nouveau, petit, vieux, vilain

Other common adjectives that PRECEDE the noun are:

autre (other), chaque (each), dernier (last), plusieurs (several), premier (first), quelque (some), quelques (pl) (some, a few), tel (such), tout (all, whole, every)

NOTE: The adjective "tout" precedes the definite article:
toute la maison = the whole house
tous les animaux = every annimal (all the animals)

Certain French adjectives have two or more meanings. In their usual position, AFTER the noun, they have their literal meaning. BEFORE the noun, they have a different meaning.

une coutume ancienne = an old (ancient) custom
une ancienne coutume = a former custom

un garçon brave = a brave boy
un brave garçon = a fine (good, worthy) boy

une étoffe chère = an expensive material
un cher ami = a dear friend (= esteemed, cherished)

la semaine dernière = last week (= just passed)
la dernière semaine = the last week (of a series)

un auteur méchant = a spiteful (wicked, vicious, ill-natured) author
un méchant auteur = a bad (pitiful, inept) author
un méchant garçon = a bad (naughty) boy

la chose même = the very thing
la même chose = the same thing

mes gants propres = my clean gloves
mes propres gants = my own gloves

un homme seul = a man alone, a a single man (by himself)
le seul homme = the only man

Mme