要件

Apexの基本ポイント
①Countなどの集合変数
　 List<AggregateResult>
AggregateResult.get('fieldName expr0,1,2')
②Mapの使用方法
　Map<id,Account> accounts = new Map<id,Account>( [Select Id, Name from Account Where Id IN :recordIds])
map.keysets().map.values(), map.get(key)

public class AccountProcessor{
  @future
  public static void countContacts(List<Id> recordIds) {
    Map<id,Account> accounts = new Map<id,Account>( [Select Id, Name from Account Where Id IN :recordIds]);
    
    List<AggregateResult> arr = [select accountid,count(id) 
                             from contact Where accountid  IN :recordIds group by accountid ];
                             
    For (AggregateResult ar : arr){
        System.debug( ar.get('AccountId') + '---' + ar.get('expr0'));
        String accId = ar.get('AccountId').toString();
        accounts.get(accId).Number_Of_Contacts__c =  (Decimal)ar.get('expr0');
    }
    
    update(accounts.values());
  }
}

Countだけをとるとき

List<AggregateResult> arr = [Select count(id) CNT from account];
System.debug(arr.get(0).get('CNT'));

Or

AggregateResult arr0 = [Select count(id) CNT from account];
System.debug('Count:' + arr0.get('CNT'));