If a 12 year old got 110 on an adult IQ test would that translate to an IQ of 147?
No, unequivocally, no.
For two primary reasons ( and other more minor reasons):
You cannot give a 12 year old an "adult" test because you have no standardized administration and you have no comparative data for that age group. However, there is something called a "mental age," that is sometimes used with persons with mental retardation such as downs syndrome. In this case, however, it is the reverse. Instead of using an adult version on a child, you use a child version of a test with an adult, so see what their mental age is. However, you do not use an IQ test for this. There are separate cognitive tests and developmental ratings that are used for this purpose.
The second reason is that the math is off. A standard score of 110 is on the cusp of average to high average, if the test is reported in standard scores. A score of 147 (or maximum) would be a genius. A child that has an average IQ for an adult doesn't have a genius IQ. IQ isn't malleable to that extent over time. IQ is a measure of native abilities, not education or knowledge. You can't train yourself to be a genius if you were not born one.
Especially in your example, the child is 16. You can give a 16 year old an adult IQ test... if their score is 110, their score is still 110, and they'd still be average to high average.
You do not derive IQ through your formula above (score x age)/12 = score. I don't know where that formula came from but it is wrong for so many reasons, I don't have time to answer them here.