To find the conjugate of a complex number, we change the sign of its imaginary part. Step 1: Identify the complex number. 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 $b=3$. Step 2: Apply the definition of a conjugate. 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 $\boxed{4-3i}$.