To determine which of the given equations has no solution, we need to analyze each equation:
1. **Equation 1**: \(3x + 4 = 3x + 3\)
Subtracting \(3x\) from both sides gives:
\[
4 = 3
\]
This is false. Therefore, this equation has no solution.
2. **Equation 2**: \(3x + 4 = 3x + 4\)
Subtracting \(3x + 4\) from both sides gives:
\[
0 = 0
\]
This is true for all \(x\). Therefore, this equation has infinitely many solutions.
3. **Equation 3**: \(3x + 4 = 4x + 3\)
Rearranging gives:
\[
3x + 4 - 4x = 3 \implies -x + 4 = 3 \implies -x = -1 \implies x = 1
\]
This has one solution (x = 1).
4. **Equation 4**: \(4x + 3 = 3x + 3\)
Rearranging gives:
\[
4x - 3x + 3 = 3 \implies x + 3 = 3 \implies x = 0
\]
This also has one solution (x = 0).
Based on the analysis, the equation with no solution is:
**\(3x + 4 = 3x + 3\)**.