Can I lose weight simply by reducing my Fat intake?

Well, if you reduce your fat intake, and by that I mean your intake of food with high levels of fat, while keeping everything else constant, yes. But reducing your intake of fat and replacing with an equal number of calories from carbs or protein (or alcohol) will not result in weight loss, at least not beyond the initial adjustment period. That being said, high-fat foods are more calorie dense, which means you get less volume of food for the same amount of calories. Therefore, you may feel less full after a high-fat, 500 calorie meal than you would after a high carb/protein, 500 calorie meal.

However, fat (especially mono- and poly-unsaturated fats from sources like fish, avocado, and nuts) is a very important component of the diet! Don't cut it out completely- aim for 15-30% calories from fat regardless of the number of calories you consume.