LINQ depends on extension methods because they let us add new methods to existing types like IEnumerable<T> without changing their code. When we write numbers.Where(...), the compiler finds the static extension method Where that takes IEnumerable<T> as the first argument. This method returns a filtered sequence but does not create a new list immediately. Instead, it uses deferred execution, meaning the filtering happens when we iterate the result. This allows chaining multiple LINQ calls efficiently. The execution table shows creating a list, calling Where, and iterating the filtered results step by step. Variables like 'numbers' and 'evens' track the original list and the filtered sequence. Key moments clarify why Where works on List<int> and why it returns IEnumerable<T>. The visual quiz tests understanding of iteration steps and extension method requirements. Overall, extension methods are the foundation that makes LINQ's elegant syntax and behavior possible.