What's the digit "a" in this number? a and b are digits in a four-digit natural number 7a5b. If 7a5b is divisible by 18, how many different possible values can "a" have?

One way:
$$7a5b=7050+100a+b\equiv 12+10a+b\pmod{18}$$
Clearly, $b$ must be even 
and $9$ must divide $12+10a+b=12+10a+b\iff 3+a+b$ must be divisible by $9$ 
For example,
if $b=0,3+a$ must be divisible by $9\implies a=6$ as $0\le a\le9\iff3\le a+3\le12$ 
if $b=2,5+a$ must be divisible by $9\implies a=4$ 
and so on
