Im looking for a way to let external user to login to my on-premm sharepoint by useing thier google/yahoo/fb accoutns. I found many articles about using ACS and identity providers to sign in, and these articles is going direct way from user to acs.

waht i actully want is to make the sign in go throw adfs the way in this figure.

Hi Bahaa,

You are correct. ACS can be a connector between ADFS and external identity providers, and in this scenario, you should add your ADFS as a relying party of ACS, and here ADFS acts as a consumer. In next step, SharePoint consumes token service from ADFS. The following articles describe the authentication flow you expected. Please have a look:

Federated SAML Authentication with SharePoint 2010 and Azure Access Control Service
https://social.technet.microsoft.com/Forums/sharepoint/en-US/5d5beef5-c853-4607-9a0a-819bcc2d4228/federated-saml-authentication-with-sharepoint-2010-and-azure-access-control-service?forum=sharepointgeneralprevious

Setting up Windows Azure Active Directory ACS to provide identities to Windows Azure Pack
http://blogs.technet.com/b/privatecloud/archive/2014/01/17/setting-up-windows-azure-active-directory-acs-to-provide-identities-to-windows-azure-pack.aspx

Alternatively, you can switch the role of ADFS and ACS, where you simply use ACS to integrate with SharePoint, and in this scenario, ADFS is optional(as long as you want to use ADFS for on-premises Active Directory users).

Here are two articles about this scenario:

Using Azure ACS to Sign In to SharePoint 2013 with Facebook (without ADFS)
http://dannyjessee.com/blog/index.php/2012/11/using-azure-acs-to-sign-in-to-sharepoint-2013-with-facebook/

Federated SAML Authentication with SharePoint 2010 and Azure Access Control Service Part 1 (with ADFS)
https://samlman.wordpress.com/2015/03/01/federated-saml-authentication-with-sharepoint-2010-and-azure-access-control-service-part-1/

Thanks,
Reken Liu