Why can't I see the amount of troops in an enemy town sometimes in HoMM 3?

Solution 1:

What you see when you check on an enemy town is entirely dependent upon the number of Taverns that you control in your own towns.

• 0 Taverns - you will see no information about the creatures in the town.
• 1 Tavern - you will only see the types of creatures in the town.
• 2+ Taverns - you will see the types of creatures in the town and the approximate numbers of each creature.

Moving away from Taverns and switching to magic, it is possible to see the exact numbers of creatures. The second level magic spell Visions, when cast by a hero with Expert magic in any school, will show the exact type and number of creatures in an enemy town.

As your screenshot shows that you only control a single town, you can only have a single Tavern, thus all you can see at the moment is the types of creatures in the enemy town.