What is the conjugate of 3i+4 ?

The given complex number is $3i+4$.
We can write this in the standard form $a+bi$ as $4+3i$.
Here, the real part is $a=4$ and the imaginary part is $b=3$.

The conjugate of a complex number $a+bi$ is $a-bi$.
For $4+3i$, the conjugate is $4-3i$.

The conjugate of $3i+4$ is $\boxed{4-3i}$.