Temperature scale converter in Java
You can shorten that code by not converting the values directly, but rather use common intermediate representation. E.g. you could convert the incoming number first to celsius (not matter what source and destinations are) and then convert the intermediate representation to the target:

double inputTemperature = ... ;
double outputTemperature;
String inputUnit = ... ;
String outputUnit = ... ;
// input conversion if necessary
if (inputUnit.equals("fahrenheit")) {
    inputTemperature = fahrenheitToCelsius(inputTemperature);
}
if (inputUnit.equals("kelvin")) {
    inputTemperature = kelvinToCelsius(inputTemperature);
}
// output conversion:
if (outputUnit.equals("fahrenheit")) {
    inputTemperature = celsiusToFahrenheit(inputTemperature);
}
if (outputUnit.equals("kelvin")) {
    inputTemperature = celsiusToKelven(inputTemperature);
}


So only 4 if statements rather than 9.

P.S.: Please review https://stackoverflow.com/questions/513832/how-do-i-compare-strings-in-java