But I Need To Multiply Them!

$45$ is divisible by 9 y 5. Then each integer or natural number multiplied by $45$ finishes at 5 or 0, in this case it finishes at 5 ,and the sum of its digits is a multiple of 9. And digits of $\bigstar \space \bigstar \space 3 \space 5$ sum $2 \cdot \bigstar + 8$ which is a multiple of 9. Since $0 \leq \bigstar < 10$ and $\bigstar$ is a natural number, the only posibillity is $2 \cdot \bigstar + 8 = 18 \Rightarrow \bigstar = 5$

Note.- Anyway, if you want solve it quickly and good, take a calculator or by hand , and you'll find $123 \times 45 = 5535$

Can you please tell me that how do you get to know about the * numbers without multiplying ? @Pi Han Goh

Considering that 45 is divisible by 9, the partially unknown number is divisible by 9 too. This means the sum of digits is divisible by 9. The only option among 3, 4, 5 and 6 that satisfies this is $\boxed{5}$ . 5+5+3+5=18 which is divisible by 9.