"I do not know how to take care of children."

Translation: Je ne sais pas comment m'occuper d'enfants.

[rosebod]

Why is this "d'enfants" and not "des enfants"?

[Arjofocolovi]

"of children" = "de enfants" (literal translation) = "d'enfants" (correct translation)

"of the children" = "de les enfants" (literal translation) = "des enfants" (correct translation)

We use mandatory contractions for these cases.

Please do not confuse this "des" with the indefinite article "des" used for the plural of "a/an" in English, see below.

• "Nous avons des jouets." = "We have toys"
• "Prends bien soin des jouets." = "Take good care of the toys."

[maggimunro]

Would soigner be acceptable here?

[Arjofocolovi]

Not really, "soigner" usually conveys a sense of "healing" or "treating" diseases, sufferings, wounds, etc...

"soigner" can also be used when we pay close attention to something to be sure it's perfectly in place or in order, like our own clothes for example, or a haircut.