The way i approached it is following:

We have total of 12 people.

M1 W1 M2 W2 ...... M6 W6

number of ways to choose 4 people out of 12 is 12C4 = 495

Let's say first place goes to M1.

second place can go to anybody except for W1. number of ways = 10.

third place can go to any of the remaining 8 people. number of ways = 8.

fourth place can go to any of the six eligible people. number of ways = 6.

I am not sure whether this is the right approach. If yes, how should i proceed further?

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keeps making mistakes and succeeds..