How many six digit even numbers can be formed with 1, 3, 4, 6, 7, 9? (no repetition)

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I'm trying to figure out how to do this permutation task.

So I have the numbers 1, 3, 4, 6, 7, 9 and I need to find out the possible amount of even six digit numbers I can make with them. The numbers can't repeat themselves.

So I know that the calculation would have only two possibilities on the units slot, like

x * x * x * x * x * 2

I thought I could just fill the remaining slots with the total amount minus one and decrease afterwards, so it'd be

5 * 4 * 3 * 2 * 1 * 2

Which gives me 240, but I'm not sure if that's correct.

Is that right?