What does it mean to "Dispose of the case by the Informal Adjustment"

It means that you have been offered the option of agreeing to the terms of an "informal adjustment" of the criminal charges filed against you in the juvenile court system. That means, if you comply with the terms of the informal adjustment, your case will not be prosecuted, you will not have to appear in court to try your case, or be sentenced by the juvenile court judge. You will not be found guilty. However, the prosecutor's office will have to sign off on this arrangement (they typically do so on first offenses), and so long as you comply with all terms agreed to, your case will be closed out. You will never have to admit to any crime or ever be found guilty. If you fail to comply, then the case can be referred for prosecution. You do not, however, have to agree to the informal adjustment. You have the option to go to trial and assert your innocence, and make the State prove you guilty beyond a reasonable doubt. You have the right to be represented by a lawyer, and you should at least seek counsel's advice to determine whether you have a good defense to the charges. Having said all that, however, most juvenile defendants agree to the informal adjustment, for obvious reasons: it's a guaranteed outcome with few risks as long as you comply.