C# Online Compiler | .NET Fiddle

using System;
using System.Collections.Generic;
using System.Linq;

namespace GoogleUnitsConversion
{
    //https://medium.com/@alexgolec/google-interview-problems-ratio-finder-d7aa8bf201e3
    class Program
    {
        static (string source, string destination, double coef)[] coeffs = {
            ("foot", "inch", 12),
            ("hand", "inch", 4),
            ("mile", "foot", 5280),
            ("light year", "km", 9.461e+12),
            ("km", "mile", 0.621371)
        };
        static void Main(string[] args)
        {
            var allCoeffs = Queryable.Union<(string source, string destination, double coef)>(coeffs.AsQueryable(), coeffs.Select(s => (s.destination, s.source, 1 / s.coef))).ToArray();


            var unit1 = "hand";
            var unit2 = "light year";
            var result = SearchConversion(allCoeffs, unit1, unit2);

            Console.WriteLine(result);
        }

        private static double SearchConversion((string source, string destination, double coef)[] allCoeffs, string unit1, string unit2)
        {
            var result = 0.0;
            var conversionAdded = allCoeffs.Where(w => w.source == unit1).Select(s => (destination:s.destination, coef:s.coef)).ToDictionary(k => k.destination, e => e.coef);
            bool somethingChanged = true;
            while (somethingChanged)
            {
                somethingChanged = false;
                foreach (var existingConversion in conversionAdded.Keys.ToArray())
                {
                    var nextStep = allCoeffs.Where(w => w.source == existingConversion && !conversionAdded.ContainsKey(w.destination));
                    foreach (var newConversion in nextStep)
                    {
                        if (existingConversion == unit1) continue;
                        var newCoeff = conversionAdded[existingConversion] * newConversion.coef;
                        conversionAdded.Add(newConversion.destination, newCoeff);
                        somethingChanged = true;
                        if (newConversion.destination == unit2)
                        {
                            result = newCoeff;
                            return result;
                        }

                    }
                }
            }
            return result;
        }
    }
}

 
using System;
using System.Collections.Generic;
using System.Linq;
​
namespace GoogleUnitsConversion
{
    //https://medium.com/@alexgolec/google-interview-problems-ratio-finder-d7aa8bf201e3
    class Program
    {
        static (string source, string destination, double coef)[] coeffs = {
            ("foot", "inch", 12),
            ("hand", "inch", 4),
            ("mile", "foot", 5280),
            ("light year", "km", 9.461e+12),
            ("km", "mile", 0.621371)
        };
        static void Main(string[] args)
        {
            var allCoeffs = Queryable.Union<(string source, string destination, double coef)>(coeffs.AsQueryable(), coeffs.Select(s => (s.destination, s.source, 1 / s.coef))).ToArray();
​
​
            var unit1 = "hand";
            var unit2 = "light year";
            var result = SearchConversion(allCoeffs, unit1, unit2);

Cached Result

Magneto
Wolverine