Puzzle ZVLZ 

Workings

Hint
Look at Digit 3 first.

Answer
6394.

Reasoning
Labelling the clues:

Digit 2 is smaller than Digit 4 Digit 4 is two thirds of Digit 1 Digit 1 is two thirds of Digit 3 Digit 3 is three times Digit 2
Using (4), Digit 3 can only be 3, 6 or 9 (as it's 3 x Digit 2).

Therefore, using (4), Digit 2 can only be 1, 2 or 3.

Using (3), Digit 1 can only be 2, 4 or 6 (as it's two thirds of Digit 3).

However, using (2), the only possible value for Digit 1 that we can find two thirds of is 6.

So, using (2), Digit 4 is 4.

So far, we have 6??4.

Using (3), Digit 1 is two thirds of Digit 3, so Digit 3 must be 9.

And, by (4), Digit 2 must be 3.

Giving 6394.