Employees of a certain company are each to receive a unique 7-digit id

One can use slot method to solve this.
7 digit identification code has 7 slots to fill.
_ _ _ _ _ _ _ .
For the first slot there are three possible options. (1,2 and 3 because first digit has to be half of second)
For the second slot there are three possible options. (2,4 and 6 because second digit has to be twice the second)
To fill the first two slots there are only three possible ways. Because if the ,
if the first is 1 the second has to be 2 (only 1 way)
if the first is 2 the second has to be 4 (only 1 way)
if the first is 3 the second has to be 6 (only 1 way) . So total ways to fill first two slots = 3ways
You are now left with 5 digits and 5 slots to fill, which can be filled in 5! ways i.e. 120 ways.

Total no: of valid codes will be therefore : 120 * 3 = 360ways.

Answer : D