Why do we need to change the discountedPrice function (to returning a Double)? How if we not use a "return" in a "func"

You're returning a Double because you're dealing with prices, which have decimals. If you want a function that doesn't have a return type, just omit the arrow (i.e. "->") and return type. For example, the following function does not have a return type:

func discountedPrice(percentage: Double) {
     self.price = self.price - (self.price * percentage / 100.0)
}

That function is only modifying the "price" property of our class, which means I don't need to return a value.

When you're calling that function, you just need to call the actual method using dot notation along with the instance name. For example,

tshirt = Clothing("tshirt", price: 49.99)
tshirt.discountedPrice(50.0)

I hope this helps. For more info, you can check this out: Swift Programming Guide: Initialization Specifically, look under the subsection "Initializer Inheritance and Overriding". The document talks about overriding a superclass's init method, but you can pretty much look at it as if you're overriding a superclass's function.