Ами ти суичваш между функцийте, но никъде не ги изикваш.

function solve(input) {
    let carWash = 0;
    for (let i = 0; i < input.length; i++) {
        let command = input[i];
        let func = null;
        switch (command) {
            case 'soap':
                func = a => a + 10;
                break;
            case 'water':
                func = a => a + a * 0.2;
                break;
            case 'vacuum cleaner':
                func = a => a + a * 0.25;
                break;
            case 'mud':
                func = a => a - a * 0.1;
                break;
        }
        carWash = func(carWash);
    }
    console.log(`The car is ${carWash.toFixed(2)}% clean.`);
}

бих ти предложил и по-кратко решение:
 

function carWash (input) {
  let funcs = {
    soap: x => x + 10,
    water: x => x + x * 0.2,
    'vacuum cleaner': x => x + x * 0.25,
    mud: x => x - x * 0.10
  };
  let value = input.reduce((acc, curr) => funcs[curr](acc), 0);  
  console.log(`The car is ${value.toFixed(2)}% clean.`);
}