[SalesForce] Data in List to be assigned to multiselect picklist in apex

There are quite a few options to solve this problem.

First, there is an idea Apex Code: Implement Iterable<T> on Set<T>., which when implemented would eliminate the need for the below workarounds.

Example on Set<String>

Set<String> mySet = new Set<String>();
mySet.add('One');
mySet.add('Two');
mySet.add('Three');
System.debug('mySet= ' + mySet);

Debug:

08:53:25.1 (2682641)|USER_DEBUG|[5]|DEBUG|mySet= {One, Three, Two}

Option 1 - cast it to Iterable<T>

String mySet_Joined = String.join((Iterable<String>)mySet, ', ');
System.debug('mySet_Joined= ' + mySet_Joined);

Result:

08:53:25.1 (2944980)|USER_DEBUG|[8]|DEBUG|mySet_Joined= One, Two, Three

UPDATE re- Option 1 - see this post for more info about why (Iterable<String>)mySet should not be used.

Option 2 - convert original Set into List

String mySet_Joined_List = String.join(new List<String>(mySet), ', ');
System.debug('mySet_Joined_List= ' + mySet_Joined_List);

Result:

08:57:13.1 (2812911)|USER_DEBUG|[11]|DEBUG|mySet_Joined_List= One, Two, Three

Got my answer from this question thanks to @Anmol Kumar.

https://salesforce.stackexchange.com/a/301892/60388

Answer is below :

You need to create a query string first and then pass it to Database.query

Example

for(Group g :[SELECT ID,Name FROM Group WHERE Id IN :groupIds]) {
    groupNames.add(g.Name);
}

String value = '(\'' + String.join(groupNames, '\',\'') + '\')';
String queryString = 'SELECT Id, Name, MultiSelectPicklist__c FROM Program__c where MultiSelectPicklist__c INCLUDES ' + value;
List<program__c> newlist = DataBase.query(queryString);
system.debug('List of records: '+newlist);