How is the DLL HELL problem solved in .NET:-
In short, the dll hell problem is solved in .NET by signing the shared assemblies with strong name.
Please follow this article, to understand the process of strong naming an assembly.

In dot net all the shared assemblies are usually in the GAC. GAC stands for Global Assembly Cache. The path for GAC is C:\[OperatingSystemDirectory]\assembly. For example on my computer the path isC:\WINDOWS\assembly. The image below shows the shared assemblies in the GAC.


Only strong named assemblies can be copied into GAC. Strong named assemblies in .NET has 4 pieces in its name as listed below.
1. Simple Textual Name
2. Version Number
3. Culture
4. Public Key Token


All these four pieces put together, is called as the fully qualified name of the assembly. In the GAC image above Accessibility assembly has a version of 2.0.0.0.


Now consider the example below:
1. I have 2 applications, Application - A1 and Application - A2 which relies on the shared assemblyAccessibility.dll (Version 2.0.0.0) as shown in the image below.


2. Now, I have a latest version of Application - A2 available on the internet.
3. I download the latest version of A2 and install it on my machine. 
4. This new installation copies a newer version of Accessibility.dll into the GAC with version 3.0.0.0.
5. So, in the GAC we now have 2 versions of Accessibility.dll. 
6. Application - A1 continues to use Accessibility.dll (version 2.0.0.0) and Application - A2 uses Accessibility.dll (version 3.0.0.0) 
7. So, now the assemblies are able to reside side by side in the GAC. For this reason dot net assemblies are also said to be supporting side by side execution.