The even numbers on a die are 2, 4, and 6.
The multiples of 3 are 3 and 6.
So to get an even number or a number that is a multiple of 3, you must get
one of these: 2,3,4, or 6.
That's 4 ways to be successful out of 6 possible rolls of a die.
So the probability is 4 out of 6, or 4/6 which reduces to 2/3.
Edwin