I\'m trying to implement Google Play Services into my application.
I understand that there is a sample project named BaseGameUtils and I need to import it into my works
This looks to me like an admobs related issue. Admobs has now been integrated into the Google Play Services jar, but it looks like you are still including the separate admobs jar in you project. Both these jars contain the same class names, hence this causes your problem.
I suggest you remove GoogleAdMobAdsSdk.jar from your build path.
For more information on this problem, please look at
Multiple dex files define Lcom/google/ads/AdRequest$ErrorCode and Multiple dex files define Lcom/google/ads/AdRequest$ErrorCode