Final answer:
The problem appears to be related to Android development, with issues like Gradle sync errors, unimplemented required methods, and typos in case sensitivity. The solutions include checking the build script for errors, implementing the missing methods, and correcting the case-sensitive typo in the code.
Step-by-step explanation:
The issues described, such as Gradle not syncing, missing methods to implement, and typos like View.OnClickListener written as view.OnClickListener, are related to software development, most likely Android development using Java or Kotlin. The 'Gradle not sync' issue can occur when the project's build configurations are incorrect or Gradle cannot download the required dependencies. This can be resolved by checking the build script for errors and ensuring all dependencies are correctly listed and available.
Similarly, 'missing methods to implement' suggests that there may be interfaces or abstract classes that require certain methods to be defined. This can be fixed by implementing the necessary methods in the classes that are supposed to fulfill the contract dictated by those interfaces or abstract classes.
The typo 'view.OnClickListener' should be corrected to 'View.OnClickListener' since Java is case-sensitive, and class names typically start with a capital letter.