It has to be a multiple of 5.  All multiples of 5 either 
end in 0 or 5.  Since it has to be even it has to end in 0,
since if it ended in 5 it would be odd.

Therefore the answer to this 

must be 0, because the digit on the right end of the number is the
ones digit.

Since it ends with a zero it is divisible by 10. So if you divide 
it by 10, the quotient will be a 2-digit number which is the same 
as the number without the 0 on the right end.  

But the quotient will still be divisible by 3.   

So the number could be any two digit number that is a 
multiple of 3 with a 0 on the right end of it for its ones digit.  

The smallest 2-digit number that is a multiple of 3 is 12, so the 
smallest the number could be is 120.  

The largest 2-digit number that is a multiple of 3 is 99, so the 
largest the number could be is 990. 

So it could be any of these thirty 3-digit numbers:

120, 150, 180, 210, 240, 270, 300, 330, 360, 390,
420, 450, 480, 510, 540, 570, 600, 630, 660, 690,
720, 750, 780, 810, 840, 870, 900, 930, 960, 990.

Edwin