Hi All , 

I  tried test class for Error (Both  DisplayErrorMsg and Checkmail) method but it didn't work.

Apex class

    public void DisplayErrorMsg(){
           
        String phone = con.Prod_Mobile__c;
        system.debug('@@phone'+phone);
        if(phone.length() == 8 && (phone.startsWith('6') || phone.startsWith('8') || phone.startsWith('9'))){
            system.debug('if loop');
            //ApexPages.addmessage(new ApexPages.message(ApexPages.severity.Error, 'Invalid Contact No. Please enter a valid mobile no (8 digits, starts with 6, 8 or 9)'));
        }
        else{
            ApexPages.addmessage(new ApexPages.message(ApexPages.severity.Error, 'Check your phoine'));
              system.debug('else loop');
        }
    }
    public void checkEmail(){
        string emailVal = con.Prod_Email__c;
        system.debug('@@email'+emailVal);
        if(!Pattern.matches('[a-zA-Z0-9._-]+@[a-zA-Z]+.[a-zA-Z]{2,4}[.]{0,1}[a-zA-Z]{0,2}', emailVal))
        {
            EmailerrorMessage = 'Invalid email address entered.';
            ApexPages.addmessage(new ApexPages.message(ApexPages.severity.Error, 'Check your email'));
        }
    }
}


test class :
@isTest
public class ContactUsThankYouControllerTest {

     static testMethod void TestMethod2() 
    {
        ContactUs_Enquiry__c con = new ContactUs_Enquiry__c();
        insert con;
        con = [select Id,Name from ContactUs_Enquiry__c where id = : con.id];
        PageReference pageRef = Page.ContactUsMain;
        Test.setCurrentPage(pageRef);
        ApexPages.Standardcontroller sc = new ApexPages.Standardcontroller(con);
        ApexPages.currentPage().getParameters().put('Id',con.id);
        
    }
    static testMethod void TestMethod1(){
           ContactUs_Enquiry__c con = new ContactUs_Enquiry__c();
        ApexPages.StandardController sc = new ApexPages.StandardController(con);
        ContactUsThankYouController obj = new ContactUsThankYouController(sc);
        con.Prod_Mobile__c = '95473732';
        con.Prod_Email__c = 'test@gmail.com';
        con.Cust_Email__c = 'test';
          obj.DisplayErrorMsg();
        obj.checkEmail();
               }            
}


Thanks,
Anish