If 12345a is a multiple of 3, then sum of its digits should be divisible by 3.
Sum of digits = 1+2+3+4+5+a=15+a
Since 15 is divisible by 3, a must be divisible by three. So a is either 0 or a multiple of three(less than or equal to 9 as a is a single digit)
So possible values of a: 0, 3, 6, 9