Let's say we have two phrases       das Auto (neutral, singular) auto   correct: Ich schenke ihm mein neues Auto. incorrect: Ich schenke ihm mein neuen Auto. I give him my new car.

If we want to check which of the two phrases is the correct one, we best check the corresponding table. We need the following information:

What's before the adjective? possessive pronoun.
Gender and number? neutral, singular
Which declension? direct object (= Accusative)

Checking the table we'll find the right ending.

Endings of the declensions with possessive pronouns neutral singular plural masculine singular plural feminine singular plural   Nominative -es -en Nominative -er -en Nominative -e -en   Genitive -en -en Genitive -en -en Genitive -en -en   Dative -en -en Dative -en -en Dative -en -en   Accusative -es -en Accusative -en -en Accusative -e -en

We have again two phrases.       der Bleistift (masculine, singular) pencil   die Bleistifte (masculine, plural) pencils   correcto: Ich gebe ihm gelbe Bleistifte. incorrecto: Ich gebe ihm gelben Bleistifte. I give him yellow pencils.

If we want to check which of the two phrases the correct one is, we best check the corresponding table. We need the following information:

What's before the adjective? nothing
Gender and number? masculine, plural
Which declension? direct object (= Accusative)

Checking the table we'll find the right ending.

Endings of the declensions without article neutral singular plural masculine singular plural feminine singular plural   Nominative -es -e Nominative -er -e Nominative -e -e   Genitive -en -er Genitive -en -er Genitive -er -er   Dative -em -en Dative -em -en Dative -er -en   Accusative -es -e Accusative -en -e Accusative -e -e

Another example       die Banane (feminine, singular) banana   die Bananen (feminine, plural) bananas   correcto: Das Zimmer verströmte den Duft süßer Bananen. incorrecto: Das Zimmer verströmte den Duft süße Bananen. The room exuded the scent of sweet bananas.

If we want to check which of the two phrases the correct one is, we best check the corresponding table. We need the following information:

What's before the adjective? nothing
Gender and number? feminine, plural
Which declension? Genitive

Checking the table we'll find the right ending.

Endings of the declensions without article neutral singular plural masculine singular plural feminine singular plural   Nominative -es -e Nominative -er -e Nominative -e -e   Genitive -en -er Genitive -en -er Genitive -er -er   Dative -em -en Dative -em -en Dative -er -en   Accusative -es -e Accusative -en -e Accusative -e -e