Why ?
When I was trying to update the NuGet Packages for one of my Xamarin projects, I got an error saying “Unable to resolve dependencies.” and the packages wasn’t updated.
The detailed error message is …
Unable to resolve dependencies. ‘Xamarin.Android.Support.Design 25.3.1’ is not compatible with ‘Xamarin.Forms 2.3.4.231 constraint: Xamarin.Android.Support.Design (= 23.3.0)’.

Image 1 : Error
The reason for the error was…
The Android project of my Xamarin solution has been configured to Compile using Android 6.0(Marshmallow) API 23.3.0 . But I was trying to update the Android packages for Android 7.1 (Nougat) API 25.3.1.

Image 2 : Current Android application properties(Compile using Android 6.0)
So the target compilation version is not compatible with the updating version of Android packages.
How To Fix the Error ?
To fix the error we have to change the target framework for compile to “Android 7.1(Nougat)”.
Here are Steps to change the target compile framework..

Image 3 : Right Click on Android Project -> Properties

Image 4 : Current Android application properties(Compile using Android 6.0)

Image 5 : Change Compile Android Version to Android 7.1 (Nougat)
When Change the target compilation version of Android , Visual Studio will ask you to restart the project to configure itself…

Image 6 : “Yes” to close and reopen

Image 7 : App is loading

Image 8 : Again go to NuGet package manager to update Android packages

Image 9 : Select Android Packages v.25.3.1(or the package showing here)

Image 10 : Accept to Agree licence and tearms

Image 11 : You can see changes will be happening (the old packages and new packages). Click OK.

Image 12 : Then the packages will be downloaded and Install Successfully.
Then Re-Build the project and the app will run successfully…
Thanks !