trigger Update_Opp_BASSENT on Task (after insert) {
public integer count;
Set<ID> Task_whatids=new Set<ID>();

for(Task T1:trigger.new)
{
Task_whatids.add(T1.WhatId );
}
system.debug('taskid'+Task_whatids);

opportunity []Oppids=[select id,BAS_Sent_Date__c,StageName from opportunity where id in:Task_whatids and RecordType.name='Group Sales KZ'];


for(Task T1:trigger.new)
{
try{

for(opportunity o:Oppids)
{

if(T1.WhatId == o.id && (T1.Subject).startsWith('Email: BAS') ){

if(o.StageName =='Booking Acknowledged'){
o.BAS_Sent_Date__c=date.valueof(T1.CreatedDate);
o.StageName='Booking Verified';

}}

}
}catch(Exception e){system.debug('Exception Here'+e);}

}
update oppids;
}

testcase

@isTest
private class Update_Opp_BASSENT_TC{

/**
* @description : Initialization of Objects and methods used in the Class
*/
static testmethod void Test(){

test.starttest();
/*
Account_Running_Number__c ar= new Account_Running_Number__c();
ar.Running_Number__c='1';
ar.Type__c='school';
insert ar;


Account cus1 = new Account();
cus1.LastName = 'asdasd';
cus1.phone='7522455';
cus1.ParentId=NULL;
cus1.Type1__c='school';
cus1.Business_Registration_Number__c='dddee';
cus1.BillingCountry='malaysia';
cus1.BillingState='Johor';
insert cus1;
*/

Opportunity opp = new Opportunity();
opp.Name = 'test';
opp.StageName = 'Needs Analysis';
Opp.closedate = date.ValueOf('2009-09-21');
opp.StageName='Booking Verified';
insert opp;

contact c= new contact();
c.lastname='teeet';
insert c;

Task t = new Task();
t.subject = ' Email: BASaaaa';
t.WhatId= opp.id;
t.status = 'open';
t.description = 'ddd';
insert t;

Task t1= new Task();
t1.subject = ' BASaaa';
t1.WhatId= opp.id;
t1.status = 'open';
t1.description = 'ddd';
insert t1;
test.stoptest();
}
}