Could you make things a little easier on those wishing to help by showing us exactly what line(s) of code have an issue and the error(s), if any, that you receive?
From the looks of things though, my guess is you're having issues with your showKiloMeters, showInches and showFeet methods. If this is correct it's because your "meters" variable is declared inside of your "main". This means that the "meters" variable is not visible to any code outside of your main method (i.e. showKiloMeters, showInches and showFeet). For further reading google something along the lines of "java variable scope".
To fix your issue I see a couple possibilities.
1. Make meters a class variable so that all methods in the class can see and access it.
public class meterProblem
//If declared here, your show methods should be able to access meters
double meters; // A number entered by the user
public static void main(String  args)
int number; //selection by the user
2. Leave the meters variable declared in "main", but pass it to your show methods so that they can access it
public static void showKiloMeters(double meters)
public static void showInches(double meters)
public static void showFeet(double meters)