Check if a string list contains any substrings from another string list

var result = list1.Any(s1 => list2.Any(s2 => s1.Contains(s2)));

or, using more tricky syntax

var result = list1.Any(s1 => list2.Any(s1.Contains));

If you want to have just bool result - if any string (say, "fou") within secondList contains in any item within firstList (say, four: four) - you can try

  List<string> firstList = new List<string>() {
    "five", "four", "three", "two", "one",
  };

  List<string> secondList = new List<string>() {
    "bathroom", "twelve", "thirteen", "fou",
  };  

  ...

  bool result = secondList
    .Any(second => firstList.Any(first => first.Contains(second))); 

var list1 = new List<string> { "five", "four", "three", "two", "one" };
var list2 = new List<string> { "bathroom", "twelve", "thirteen", "fou" };
var found = list1.Any(i1 => list2.Any(i2 => i1.Contains(i2)));

EDIT

Based on your comments, I understand that you are having trouble debugging. You can extend the above code like for example below, so it helps you better understand what the code is doing:

var list1 = new List<string> { "five", "four", "three", "two", "one" };
var list2 = new List<string> {  "f", "o", "t" };
var found = list1.All(i1 =>
    { 
        var l1Result = list2.Any(i2 => 
            {
                var l2Reuslt = i1.Contains(i2);
                Console.WriteLine($"{i1} constains {i2}: {l2Reuslt}");
                return l2Reuslt;
            });
        Console.WriteLine($"{i1} Final : {l1Result}");
        return l1Result;
    }
);