Why does 7+5=12 is considered "synthetic a priori" by Kant?
According to Kant, analytic statements really tell us nothing new about the world: they simply assert a structural relationship between subject and predicate, i.e., a predicate that is already "contained" in the subject as part of its meaning. They are "analytic" in the sense that the predicate can be found by analyzing the meaning of the subject. All bodies are extended is analytic because part of the definition of a body is that it occupies space (which is what "extended" means here). This statement clarifies what we already understand a body to be, but does not tell us anything more about them.
"All bodies are heavy" is synthetic because "having weight" is not part of the definition of "occupying space." In addition,
Take a look at this:
7+5= 12 (one had to add them)
24 - (2x6) = 12 (less obvious)
Actually I can have an infinite number of combinations on the right hand side of the equation that equals 12.
Same with "straight line" and "two points" and "shortest line" and "two points", neither of which can be analytically "extracted" from the other.