The sum of the interior angles of a polygon is (n-2)180°

So the sum of the interior angles of a hexagon (which has n=6 sides)
is (6-2)180° = (4)180° = 720°

Let the angles in the ratio 1:2:4 be x°, 2x° and 4x°

Let the three congruent angles each have value y°

So the 6 angles are

x°, 2x°, 4x°, y°, y°, y°

Then the sum of the 6 angles is

x° + 2x° + 4x° + y° + y° + y° = 720°

                      7x + 3y = 720 

So there are lots of possible answers.

For example if you choose x° to be 30° you will get

                     7(30) + 3y = 720
                       210 + 3y = 720
                             3y = 510
                              y = 170

So the 6 angles will be

 x°,  2x°,  4x°,   y°,   y°,   y°
30°,  60°,  90°, 170°, 170°, 170°

But if you choose x to be 36° you will get

                     7(36) + 3y = 720
                       252 + 3y = 720
                             3y = 468
                              y = 156

 So the 6 angles will be:

 x°,  2x°,  4x°,   y°,   y°,   y°
36°,  72°, 108°, 156°, 156°, 156°

And if you choose x to be 42° you will get

                     7(42) + 3y = 720
                       294 + 3y = 720
                             3y = 426
                              y = 142

 So the 6 angles will be:

 x°,  2x°,  4x°,   y°,   y°,   y°
42°,  84°, 168°, 142°, 142°, 142°

So your problem has many many different answers.  

Did you leave something out?

Edwin