SOLUTION: the product of 3 consecutive even natural numbers divided by their sum is 64. what is the middle number?

Let x be that middle number.
Then the three numbers are (x-2), x, and (x+2).

Their product is P = (x-2)*x*(x+2) = x*(x^2 - 4).
Their sum is S = (x-2) + x + (x+2) = 3x.
The equation is 

 = 64,  or  = 64,  or   = 64.


 = 64*3 = 192,   = 192 + 4 = 196,  x = +/-14.

Since the condition talks about natural numbers, only positive value is the solution.

Answer. x = 14.