I strongly suspect that Base.cs (the only C# file shown in the VDB.Common.RequestAndResponses project) doesn't actually declare a type in the VDB.Common.RequestAndResponses namespace - or that it only declares an internal (rather than public) type.
For example, note that the code you're creating is under the VDB.Client.Infrastructure project, but is only declaring a class in the Agatha namespace - not VDB.Client.Infrastructure.Agatha, which may be what you were intending. Do you have the same kind of thing in Base.cs, perhaps?
Without seeing the code in Base.cs, we can't see what's wrong though. If you could just post a snippet of that - just the namespace and class declaration - that would be helpful.
Note that although a class library has a default namespace, this isn't prepended to whatever the source file actually declares. In other words, in a library of Acme.Widgets, if you had a declaration of:
namespace Web
{
    public class Button {}
}
that would only declare the type Web.Button, not Acme.Widgets.Web.Button.
EDIT: The OP's "answer" confirms what I thought... basically it's not declaring a namespace at all. It should look like this:
using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using Agatha.Common;
namespace VDB.Common.RequestAndResponses
{
    public abstract class BaseRequest :Request
    {
        // Code
    }
    public abstract class BaseResponse : Response
    {
        // Code
    }
}
I would also strongly advise that these classes should be put in two separate files, BaseRequest.cs and BaseResponse.cs. I'm also pretty surprised to see a reference to Agatha.Common - shouldn't that be VDB.Common.Agatha or something like that?