What is the missing digit?

Let's split $6=2 \times 3$ which means $\overline{5228a}$ is a even number & divisible by 3.

If you want $\overline{5228a}$ to be visible by 3,then we use $5+2+2+8=17$ to know $a=1,4,7$

If you want $\overline{5228a}$ to be a even number, then $a=0,2,4,6,8$

Combine these algebra,we have $a=\color{#3D99F6}\boxed{\large{4}}$

$\because$ the all multiple of 6 must be the multiples of $\text{}(2,3)$ .

Hence we have :

$\text{}52280$ $\rightarrow$ cannot be a multiple of 6 .

$\text{}52282$ $\rightarrow$ cannot be a multiple of 6 .

$\text{}52284$ $\rightarrow$ can be a multiple of 6 .

$\text{}52286$ $\rightarrow$ cannot be a multiple of 6 .

$\text{}52288$ $\rightarrow$ cannot be a multiple of 6 .

Note: The missing digit should be even if it be a multiple of 2 .

Since 5228? is a multiple of 6, then it must be a multiple of 2 and a multiple of 3.

If it is a multiple of 2, the digit represented by ? must be even.

If it is a multiple of 3, the sum of its digits is divisible by 3.

The sum of its digits is 5 + 2 + 2 + 8 +? = 17 + ?

Since ? is even, the possible sums of digits are 17, 19, 21, 23, 25 (for the possible values 0, 2, 4, 6, 8 for ?)

Of these possibilities, only 21 is divisible by 3, so ? must equal 4.

We can check that 52 284 is divisible by 6.