In which case did the Court first reason that "preponderance of evidence" is NOT a sufficient basis for a decision when youths are charged with acts that would be criminal if committed by adults?

The correct answer to the following question will be "In re Winship ".

Explanation:

The Due Process provision prevents the convicted from conviction unless on the evidence of that same evidence sufficient to prove the accusation of the offense beyond the preponderance of the evidence.In the context of In re Gault, the Supreme court of the U.S has decided that a minor had the right to due process, so if the offender does not manage one, one must be named.

Therefore, it's the right answer