CRT with non-coprime moduli

Compatibility. $\gcd(6,9)=3$. Need $4\equiv7\pmod3$: $4-7=-3\equiv0\pmod3$. Compatible.

Solve. From the first, $x=4+6k$. Substitute: $4+6k\equiv7\pmod9$, so $6k\equiv3\pmod9$. Divide by $3$: $2k\equiv1\pmod3$, so $k\equiv2\pmod3$, $k=2+3m$. Then $x=4+6(2+3m)=16+18m$.

Conclusion. $x\equiv16\pmod{18}$.

Check. $16\equiv4\pmod6$, $16\equiv7\pmod9$. Correct.