How to exchange data between view controllers?

I have PurchaseViewController with purchase buttons. I need to show the controller with a simple parents check (ParentsVerificationController) if the user taps one of the buttons in PurchaseViewController. If verification in ParentsVerificationController was completed successfully, I need to return to PurchaseViewController and finish the purchase. I use this code:

PurchaseViewController:

verificationState == false

@objc func weeklyButtonAction() {
        let detailController = SLVerification()
        detailController.modalPresentationStyle = .overFullScreen
        self.present(detailController, animated: false, completion: nil)
        
        if verificationState == true {
            print("good")
        }
    }
    
    @objc func monthlyButtonAction() {
        let detailController = SLVerification()
        detailController.modalPresentationStyle = .overFullScreen
        self.present(detailController, animated: false, completion: nil)
        
        if verificationState == true {
            print("good")
        }
    }
    
    @objc func annualButtonAction() {
        let detailController = SLVerification()
        detailController.modalPresentationStyle = .overFullScreen
        self.present(detailController, animated: false, completion: nil)
        
        if verificationState == true {
            print("good")
        }
    }

ParentsVerificationController:

@objc func buttonAction(sender: SLButton!) {
        switch (sender.tag) {
        case 0: if buttonsArray[0] == a {
            print("success")
            let presenter = PurchaseController()
            presenter.verificationState = true
            dismissVerification()
        } else {
            print("failure")
            shakeAnimation()
            dismissVerification()
        }
        case 1: if buttonsArray[1] == a {
            print("success")
            let presenter = PurchaseController()
            presenter.verificationState = true
            dismissVerification()
        } else {
            print("failure")
            shakeAnimation()
            dismissVerification()
        }
        case 2: if buttonsArray[2] == a {
            print("success")
            let presenter = PurchaseController()
            presenter.verificationState = true
            dismissVerification()
        } else {
            print("failure")
            shakeAnimation()
            dismissVerification()
        }
        case 3: if buttonsArray[3] == a {
            print("success")
            let presenter = PurchaseController()
            presenter.verificationState = true
            dismissVerification()
        } else {
            print("failure")
            shakeAnimation()
            dismissVerification()
        }
        default: print("error")
        }
    }

I return to PurchaseViewController with "success" but if else statement in weeklyButtonAction, monthlyButtonAction and annualButtonAction doesn't call. I can't see "good". How to fix it?

Everytime buttonAction called, you are creating a new PurchaseController therefore, you are not notifing changes to the old PurchaseViewController. To fix your problem, I recommend using delegate pattern:

class ParentsVerificationController {
    weak var delegate: ParentsVerificationControllerDelegate?
    @objc func buttonAction(sender: SLButton!) {
        switch (sender.tag) {
        case 0:
            if buttonsArray[0] == a {
                delegate?.didVerificationSuccess()
                dismissVerification()
            } else {
                shakeAnimation()
                dismissVerification()
            }
            ...
        }
    }
}


class PurchaseViewController {
    @objc func weeklyButtonAction() {
        let detailController = ParentsVerificationController()
        detailController.delegate = self
        detailController.modalPresentationStyle = .overFullScreen
        self.present(detailController, animated: false, completion: nil)
    }
}

extension PurchaseViewController: ParentsVerificationControllerDelegate {
    func didVerificationSuccess() {
        print("good")
    }
    
}

An alternative for delegate in Swift is using closure:

class ParentsVerificationController {
    var didVerificationSuccess: (() -> Void)?
    @objc func buttonAction(sender: SLButton!) {
        switch (sender.tag) {
        case 0:
            if buttonsArray[0] == a {
                didVerificationSuccess?()
                dismissVerification()
            } else {
                shakeAnimation()
                dismissVerification()
            }
            ...
        }
    }
}


class PurchaseViewController {
    @objc func weeklyButtonAction() {
        let detailController = ParentsVerificationController()
        detailController.didVerificationSuccess = {
            print("good")
        }
        detailController.modalPresentationStyle = .overFullScreen
        self.present(detailController, animated: false, completion: nil)
    }
}