The image shows three parallel lines, $r \parallel s \parallel t$, crossed by two diagonals, creating corresponding angles. To solve for $x$, we can use the properties of parallel lines and transversals.

Step-by-step solution:

1. Identify corresponding angles: Since the lines are parallel, the angles on opposite sides of the transversal and between the parallel lines are equal.

   • The angle labeled $x - 3$ is corresponding to the angle labeled $x$.
   • The angle labeled $x - 2$ is corresponding to the angle labeled $x - 4$.

2. Set up the equations based on corresponding angles:

   • $x - 3 = x$ (equating the angles formed by the transversal crossing lines $r$ and $s$)
   • $x - 2 = x - 4$ (equating the angles formed by the transversal crossing lines $s$ and $t$)

3. Solve the equations:

   • From $x - 3 = x$, we have: $x - 3 = x \implies -3 = 0$ This equation is not valid, meaning something may have gone wrong here, likely due to the fact that they are not supposed to be directly equal.

   • From $x - 2 = x - 4$, we solve: $x - 2 = x - 4 \implies -2 = -4$ This also doesn't provide a valid solution, indicating another potential error.

Given these invalid conclusions, let me rework through