A train car held $6000$ pounds of mud which was $88$ percent water. Then the train car sat in the sun, and some of the water evaporated so that now the mud is only $82$ percent water. How many pounds does the mud weigh now?
1. Initially, the train car held $6000$ pounds of mud, which was $88\%$ water. This means that $12\%$ of the mud was not water.
   \[
   \text{Weight of non-water mud} = 12\% \times 6000 = 0.12 \times 6000 = 720 \text{ pounds}
   \]

2. After some water evaporated, the mud is now $82\%$ water. This means that $18\%$ of the mud is not water. Let $x$ be the total weight of the mud after evaporation.

3. The weight of the non-water mud remains the same, which is $720$ pounds. This $720$ pounds now constitutes $18\%$ of the total weight $x$.
   \[
   18\% \times x = 720
   \]
   \[
   0.18x = 720
   \]

4. Solving for $x$:
   \[
   x = \frac{720}{0.18} = 4000 \text{ pounds}
   \]

The final answer is $\boxed{4000}$