!-- Visualforce page code --!
<apex:page controller="sampleCon">
    <apex:form >
        
    
    <apex:selectList id="ddlVCs" label="Vertical Unit / Accounts" value="{!SelectedVCs}" >
          <apex:selectOptions value="{!ValueCorridors}"></apex:selectOptions>
          <apex:actionSupport event="ondblclick" action="{!FetchAccountsForVC}" rerender="out1" status="myStatus1" />
          <apex:actionStatus id="myStatus1" startText="Please Wait..."  />
      </apex:selectList>
    
    <apex:outputPanel id="out1"   >
        <apex:selectList id="ddlAccounts" label="Accounts" value="{!SelectedAccounts}">
            <apex:selectOptions value="{!AccountsList}"></apex:selectOptions>
        </apex:selectList>
    </apex:outputPanel>
    
</apex:page>

!-- Controller Class Code --!
public class sampleCon {
    String selVCs;
    String[] selectedAccounts = new String[]{};
    List<SelectOption> lstAccountsForVC = new List<SelectOption>();
    String TempVar;
            
    public PageReference test() {
        return null;
    }

    public List<SelectOption> GetValueCorridors()
    {
        List<Account> lstVC = [SELECT Value_Corridor__c FROM Account where Business_Unit__c = 'Business Unit UK (BU-UK)'];
        
        List<SelectOption> options = new List<SelectOption>();
        
        If(lstVC.size() > 0)
        {
            for(Account Acc : lstVC)
            {
                options.add(new SelectOption(Acc.Value_Corridor__c, Acc.Value_Corridor__c));
            }
        }
        
        return options;
    }
    
    public String getSelectedVCs()
    {
        return selVCs;
    }
    
    public void setSelectedVCs(String SelectedVCs)
    {
        this.selVCs = SelectedVCs;
    }
    
    public PageReference FetchAccountsForVC()
    {
        TempVar = selVCs;
        List<Account> lstAccounts = [SELECT Id, Name FROM Account where Value_Corridor__c = :selVCs];
        
        List<SelectOption> options = new List<SelectOption>();
        
        If(lstAccounts.size() > 0)
        {
            for(Account Acc : lstAccounts)
            {
                options.add(new SelectOption(Acc.Id, Acc.Name));
            }
        }
        
        lstAccountsForVC = options;
        
        return null;
    }
    
    public List<SelectOption> getAccountsList()
    {
        return lstAccountsForVC;
    }
    
    public String[] getSelectedAccounts()
    {
        return selectedAccounts;
    }
    
    public void setSelectedAccounts(String[] SelectedAccounts)
    {
        this.selectedAccounts = SelectedAccounts;
    }    
    
}