Are you trying to say the adult age or the age of accountability would either be around age 20 or in the teens? Are you also saying that the Bible doesn't mention a specific age of accountability? What age do you believe it is? Because some people don't understand when they are teens. Some people don't understand when they are 20. Some don't understand until round 23.
The Bible doesn't speak of a particular age when a child becomes knowledgeable of good and evil. I suspect that it is because it varies from child to child. Speak to a child of seven about what makes something sinful and you will get broad answers that generally encompasses the idea that Mom and Dad don't approve of it. Speak to an eighteen-year-old and you find not only the concept of right and wrong but that he as an individual must chose between the two. When does the shift occur? I'm not really certain, but I've noticed that it often comes around the time of puberty in many people.
To speak of the age at which a person is considered an adult is not the same as the age at which a person is considered accountable. When we talk about an age of accountability, we are discussing when a person matures enough to be able to distinguish between right and wrong. Or another way to put it, the age when a person understand enough about good and evil to be held accountable for the choices that he makes. When God condemned the Israelites to wander in the wilderness for 40 years, He did not hold the children responsible for the choices made by the adults. "Moreover your little ones and your children, who you say will be victims, who today have no knowledge of good and evil, they shall go in there; to them I will give it, and they shall possess it" (Deuteronomy 1:39). Notice that the distinguishing characteristic was their knowledge of good and evil. At this particular time, God set the limit at those 20 years old or greater to be held accountable for the rebellion against going into the land of Canaan. "Say to them, 'As I live,' says the LORD, 'just as you have spoken in My hearing, so I will do to you: The carcasses of you who have complained against Me shall fall in this wilderness, all of you who were numbered, according to your entire number, from twenty years old and above" (Numbers 14:28-29). Is twenty an absolute fixed number? I don't think so. Instead, I believe that most people reach the point of being accountable by the time they are twenty. I'm sure that when God set this limit there were a few exceptions. Some, because of slow mental development, were not accountable even after the age of twenty. There were probably a number under twenty who were accountable. However, twenty made a good split, placing the vast majority in the correct category.
But when we speak of a person being an adult, we are talking about the time when all development is complete -- both physical and mental. This age also varies greatly from individual to individual, just as the age when puberty starts varies. Studies in recent years show that even after physical body changes have come to an end, the brain continues to develop. For example, one of the last areas that develop in a man's brain is the part that helps a person assess risk. For many men, this doesn't kick in until after age 24, and it is a major reason why auto insurance for men is higher before age 25. Young men tend to take excessive risks. But just because the brain hasn't fully developed, it doesn't imply that it hasn't developed enough for the individual to decide between good and evil.
Yes, there are a few who never fully develop mentally. Others might develop, but at a slower rate. However, for the vast majority, I think you will find that the knowledge of good and evil comes before the age of twenty. In the United States our courts struggle with this issue. Children who commit crimes before the state's age of majority are generally tried in juvenile court. Those who are older are generally tried as adults. Yet exceptions are made to this rule because the behavior of the individual indicates they understood the seriousness of their actions. So while there is a set age, the courts understand that it is not the same for every individual. In my years of preaching, I generally notice a distinct shift in moral thinking shortly after puberty. Yet, I work with teenagers who are immature in their moral thinking though their bodies have physically matured. Often these are the troubled youth, the ones who get into trouble with parents and the law. Some of it is due to a lack of teaching, but some appears to be a lack of capability to reason.