I installed Android Studio 2.1.3, and successfully created a new project (just call it ProA), it runs well in AVD. That time I had just only downloaded the SDK platform android-24. I created that project with the Minimum SDK API 14. Actually , I didn't download android-14 at that time.
Then later I downloaded android-14, android-15,android-21,android-23, tried to create a new project (call it ProB), but many errors occurred there.  
- The - MainActivity's superclass is- AppCompatActivity, but the error is- Cannot solve symbol 'AppCompatActivity'.
- There is a red line under the - @Overridetag over the- onCreate()method, saying that- Method does not override a method from its superclass
- In - onCreate()method ,the- setContentView(R.layout.activity_main)code snippet shows- Cannot resolve symbol 'R'.
- The Messages window has a error message saying
 A problem occurred configuring project ':app'.
 Could not download support-compat.aar(com.android.support:-compat:24.2.0): No cached version available for offline mode
the overall picture is like this: the overall error image(click to see)
the content of app\src\build.gradle:
apply plugin: 'com.android.application'
android {
    compileSdkVersion 24
    buildToolsVersion "24.0.1"
    defaultConfig {
        applicationId "com.example.zhangsir.aftervpn"
        minSdkVersion 14
        targetSdkVersion 24
        versionCode 1
        versionName "1.0"
    }
    buildTypes {
        release {
            minifyEnabled false
            proguardFiles getDefaultProguardFile('proguard-android.txt'), 'proguard-rules.pro'
        }
    }
}
dependencies {
    compile fileTree(dir: 'libs', include: ['*.jar'])
    testCompile 'junit:junit:4.12'
    compile 'com.android.support:appcompat-v7:24.2.0'
}
the content of gradle\build.gradle:
// Top-level build file where you can add configuration options common to all sub-projects/modules.
buildscript {
    repositories {
        jcenter()
    }
    dependencies {
        classpath 'com.android.tools.build:gradle:2.1.3'
        // NOTE: Do not place your application dependencies here; they belong
        // in the individual module build.gradle files
    }
}
allprojects {
    repositories {
        jcenter()
    }
}
task clean(type: Delete) {
    delete rootProject.buildDir
}
the screenshot of the standalone sdk manager (click to see)
modified at 2016 Aug,27
I have downloaded all the Android SDK Build-tools:
What can I do to solve this problem?
 
     
     
     
     
     
    