How to make a generic specifiable associated type in Swift?

Your exact formulation isn't allowed in Swift because the full type of an associatedtype must be known at adoption time (and Collection for an unspecified X isn't valid). If you don't care what X actually is at any point, then @JoakimDanielson's answer is the simplest and easiest - but if you do need to constrain X in some way, then you can incorporate it into the protocol by making SomeProtocol itself generic on X:

protocol SomeProtocol { // X is the primary associatedtype
    associatedtype X
    associatedtype T: Collection where T.Element == X
}

Then, to adopt:

struct SomeStruct: SomeProtocol {
    typealias T = Array
}
struct OtherStruct {
    let value: T.T
}

In use:

let s: OtherStruct = .init(value: ["a", "b", "c"])
print(s) // => OtherStruct(value: ["a", "b", "c"])

I think you can skip X in your protocol definition since it's already known that Collection is a generic type

protocol SomeProtocol {
    associatedtype T: Collection
}

And then your types can be declared as

struct SomeStruct: SomeProtocol {
    typealias T = Array
}
struct OtherStruct {
    let value: T.T
}

Example

let y: OtherStruct = .init(value: [1, 2, 3])