freeing up storage space on Iphone 6plus
Welcome to the community Joel. Unfortunately your question really hasn't provided much detail, so this answer may go into more detail than you wanted.

POP v IMAP

First of all I am guessing that you're using what's called a POP email account and that you've probably set your email clients up to not delete emails from the server. This is only a guess because your question provides little detail.

Both POP (Post Office Protocol) and IMAP (Internet Message Access Protocol) allow users to download their email from an email server. However, POP simply downloads email to your computer, and usually (but not always) deletes the email from the remote server. This is the way email accounts were always set up originally, but problems arise when you have more than one device (desktop, laptop, tablet or phone) you want to access your mail from. This means you have to delete or file or mark as read, etc etc the same email on every device.

IMAP, on the other hand allows you to keep your email on a remote server. This two-way protocol also allows you to synchronise your email among multiple devices, especially useful since most people have at least two devices - their laptop and smartphone. Basically, if you're using IMAP and mark an email as read, it gets marked as read in your web based inbox or other email clients too (because the changes are happening on the server, not just locally). However, this won’t be the case if you are using POP, because your emails are downloaded to your PC and the changes won’t reflect on the server.

However, there are reasons why you may prefer POP. For example, depending on the email server, storage space for your messages may be limited. Also, reading messages while offline requires use of your e-mail program's Offline mode (assuming it has one). And, in some cases, accessing and working with emails can be slower when using IMAP.

In summary, both protocols offer their advantages and disadvantages. Today many will argue that POP is deprecated and IMAP is the only way forward, but in reality there are still very good arguments for using POP over IMAP. In the end, it gets down to what you value personally.

Your situation

Now you should be able to see why I said I'm guessing that you're using a POP email account. Basically, if you were using an IMAP account you would have seen the emails you deleted on your desktop also disappear from your iPhone.

Now, I'm not saying you should change from POP to IMAP, I'm just explaining what has happened in your case and why.

So, if your goal was to free up space on your iPhone, then you need to do it directly on your iPhone, rather than on your desktop. However, if your goal was to reduce space on both, then you will need to do it separately on both, or consider changing your setup to use IMAP instead.

If you'd like to change your setup and need help in doing so, it'd be best to post another question providing more details of your situation and asking for advice on that.

Steve Chamber's suggestion may work

Just a quick word on Steve's comment re your question:


  The easy way would be to delete the account from the phone. That will
  remove all the data. then re-add the account and any deleted data
  won't be there.


Steve's suggestion may also help you achieve what you want if you haven't got a lot of emails still on your server. For example, if you've set up your email clients so that emails remain on the server for only a day or week after being downloaded, then Steve's suggestion may be a quick fix because your iPhone will only re-download a smaller number of emails. However, if your email clients are not deleting emails from the server, or leaving them on the server for a long time before deleting, then Steve's suggestion won't be very helpful.