Change the location of an object programmatically

Location is a struct. If there aren't any convenience members, you'll need to reassign the entire Location:

this.balancePanel.Location = new Point(
    this.optionsPanel.Location.X,
    this.balancePanel.Location.Y);

Most structs are also immutable, but in the rare (and confusing) case that it is mutable, you can also copy-out, edit, copy-in;

var loc = this.balancePanel.Location;
loc.X = this.optionsPanel.Location.X;
this.balancePanel.Location = loc;

Although I don't recommend the above, since structs should ideally be immutable.

The Location property has type Point which is a struct.

Instead of trying to modify the existing Point, try assigning a new Point object:

 this.balancePanel.Location = new Point(
     this.optionsPanel.Location.X,
     this.balancePanel.Location.Y
 );