A nominal phrase or nominal group in German and some other languages consists of a single or no determiner ‘DET’ (i.e. article ‘ART’ or pronoun ‘PRON’), possibly multiple adjective ‘ADJ’ and a noun ‘SBST’ as its head.
Some languages may show the grammatical agreement of these group members by affixing the same morpheme to all of them. German grammar does not work that way, so drop that wrong mental model now!
In German, usually the determiner of a group bears the clearest information about case, number and gender, fused into a single suffix.
It always does if it is a definite article (der/das/die) or demonstrative pronoun (dies+); adjectives are inflected “weakly” then and can only end in -e or -n.
For masculine and neuter nouns, the suffix shifts to the adjective(s) in Nom and NeutAcc if an indefinite article (ein+) or possessive pronoun (e.g. mein+) is used as determiner.
Only if the determiner is a numeral ‘NUM’ (i.e. a number or other quantifier), which is logically always plural, or is left out altogether, all markers move to the adjective(s), but the suffix changes from -s to -n for Gen Masc/Neut. They are said to inflect “strongly”. While numbers only decline in Gen, other quantifiers (viel+, einig+ …) usually inflect like the adjective.
Most nouns will exhibit case suffixes only for Gen (Masc/Neut) or Dat (Pl) or not at all (Fem), and sometimes these coincide with those of the attributes, e.g. des (schönen) Kindes and den schönen Kindern.
Unlike attributes, nouns often have a special inflection base for the plural which can be formed by umlauting their stem or acquiring a suffix or both – any case suffix follows.
While nouns do not decline by gender (except for adjectives used as nouns), their final non-inflectional morpheme always determines it, e.g. +in → Fem. This effectively includes the plural morpheme, so German never treats gender and number separately, i.e. they’re one and the same category. However, verbs change by number only, as do 1st and 2nd personal pronouns, and interrogative pronouns depend on animate state in Nom and Acc using the same morphs as Masc vs. Neut elsewhere.
Also remember that only masculine attributes may have forms for all four cases, whereas neuter and plural ones don’t distinguish Acc from Nom and feminine ones furthermore don’t distinguish Dat from Gen.