Question 481431
Recall that an even number ENDS with an even digit:  
(digit) (digit) (digit) (even)


That means that the only digits this 4-digit number could end in are 0, 2, or 6, so there are 3 options for the last digit: 
(digit) (digit) (digit) (3 options)


Once you have the last digit, you can work backwards.  You started with 6 digits, and you've used one digit.  I don't know what one it was, but it doesn't matter: you used one, so you have 5 left to choose from: there are 5 options for the next digit.  
(digit) (digit) (5 options) (3 options)


Now you've used 2 digits, so there are 4 options for the next one.  Once you've used that, you're down to 3 options for the first digit.
(3 options) (4 options) (5 options) (3 options)


To find out how many numbers you could make, you simply multiply: {{{3*4*5*3=180}}}