#### Answer

A value that gives no solution is 10; A value that gives infinitely many solutions is 20.

#### Work Step by Step

Let z be the variable for our blank;
Given the system of equations:
3x+2y=10
6x+4y=z
We know that if we set z to 10, it will have no solutions. Since 3x+2y=10, 6x+4y=10 cannot be true.
Additionally, we know that (equation 1)$\times$2 is:
6x+4y=20
Therefore, if we set z=20, the equations will be equivalent, and the system will have an infinite amount of solutions.