The linear congruence 9x≡6(mod15)9x \equiv 6 \pmod{15}9x≡6(mod15) has integer solutions if and only if:
gcd(9,15)∣6\gcd(9, 15) | 6gcd(9,15)∣6, which is true since 3∣63 | 63∣6
15∣615 | 615∣6
9 and 15 are coprime
6 is odd