I'm incredibly new to all of this so I appreciate any help you're able to offer.

I've got a Task Trigger that is firing correctly for just general tasks; however, I want to add a filter to the type of tasks that update the related whoId.  I basically only want the whoId to be updated if the task is complete and contains "Inbound" which is contained in multiple values in a single picklist.  The "Inbound" string in Step A is there because I'm not sure how to filter by the actual field.

trigger LastActivityUpdate on Task (after insert, after update) {
	        
    //Step A: Add the Inbound Set
    Set<String> Inbound = new Set<String>{'Inbound Letter', 'Inbound Email','Inbound Web', 'Inbound Call'};
    
    //Step 1: Create a set of Contact IDs from the task
    Set<String> whoIds = new Set<String>();
		//for these tasks, pull in the whoID
    	for (Task t : Trigger.new){
        //    This "Done" criteria was throwing some system exceptions so I've just got it noted.
        //      if (t.Done__c = TRUE){
            	whoIds.add(t.WhoId);
        //    }
		}
    
    //Step 2: list that Contact and their "Last Inbound Activity" field
    List<Contact> cons = [SELECT Id, Last_Inbound_Activity__c FROM Contact WHERE Id =: whoIds];
    
    //Step 3: iterate over tasks and create map of tasks by WhoId
    Map<String, Task> taskMap = new Map<String, Task>();
    	for (Task t : Trigger.new){ 
			taskMap.put(t.whoID, t);
			}
    
	//Step 4: iterate over Contacts, retrieve fields and set with ActivityDate
    for (Contact c : cons) {
        if (taskMap.containsKey(c.Id))
    		c.Last_Inbound_Activity__c = taskMap.get(c.Id).ActivityDate;
  		}  
    
    //Lastly, update the contact
    update cons;
}