Step 1: Draw m-cresol.
m-cresol is 3-methylphenol. The -OH sits on carbon 1 and the methyl group sits on carbon 3. Both -OH and -CH$_3$ are activating groups that send incoming groups to ortho and para spots.
Step 2: Find where nitration goes.
The -OH directs strongly to positions 2, 4 and 6. The methyl at C3 directs to positions 2, 4 and 6 as well. The two groups agree best on positions 4 and 6, which are open and not crowded.
Step 3: Place the two nitro groups.
So the two -NO$_2$ groups go to carbon 4 and carbon 6, while -OH stays at 1 and -CH$_3$ stays at 3.
Step 4: Name the product.
With -OH as the main group at C1, we have methyl at 3 and nitro groups at 4 and 6. That is 3-methyl-4,6-dinitrophenol.
Step 5: Conclusion.
So the answer is 3-methyl-4,6-dinitrophenol. \[ \boxed{\text{3-methyl-4,6-dinitrophenol}} \]