Hoi have got speed dial on the main switchboard, so how do i do speed dial from other extensions

Not normally, because would you want Julie in Accounting speed dialling your Husband by mistake. Making wide assumption you are female, but you get the drift. Manuals and video in the link.

https://www.google.com/search?q=setup+the+speed+dial+on+the+main+set+of+the+PABX+KX-TEM824+can+i+use+the+speed+dial+on+the+extensions

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If you are a home user, then no. If you are in an office that has a switchboard and the fax uses an extension from the switchboard then yes ( it may on some systems be a 1 or a 3 instead of 9).
If you are in an office and the fax has its own line then again no. Its easier to just an ordinary phone into the socket and see which way works.

It sounds as if you have DND - Do Not DISTURB
feature turned on...

There should be a light or indicator on the STATION itself
giving the DND status.

Carnac the Magnificent

Perhaps you are trying to set up speed dialing.
Right?

If you are using the KX-T7730 phone on a Panasonic KX-Txx 308 or 824 system.
From the Switchboard / Main telephone ( usually ext 101, 10 or 9 ) with the handset on the cradle/hook :
1. Press PROGRAM * # followed by the system password ( default is 1234).
2. Now press 604 and then SP-PHONE. Enter the jack number you wish to change ( 01 is extension 101, 02 is extension 102 etc. ).
3. Enter the name ( basically the same as texting on a cellphone ). Press AUTO DIAL / STORE to save your change.
4. To go to the next extension press SP-PHONE. Don’t forget to press AUTO DIAL / STORE to save your change after each name entered.
5. Press PROGRAM to exit program mode and you are done.

If you are using the KX-T7730 phone on a Panasonic KX-Txx 308 or 824 system. From the Switchboard / Main telephone ( usually ext 101, 10 or 9 ) with the handset on the cradle press PROGRAM * # followed by the system password ( default is 1234). Now press 604 and then SP-PHONE. Enter the jack number you wish to change ( 01 is extension 101, 02 is extension 102 etc. ). Enter the name ( basically the same as texting on a cellphone ). Press AUTO DIAL / STORE to save your change. To go to the next extension press SP-PHONE. Don’t forget to press AUTO DIAL / STORE to save your change after each name entered. Press PROGRAM to exit program mode and you are done.
PLEASE rate / vote this answer if it was helpful.
Thank you.

I assume that you want to program the extension names.

If you are using the KX-T7730 phone on a Panasonic KX-Txx 308 or 824 system. From the Switchboard / Main telephone ( usually ext 101, 10 or 9 ) with the handset on the hook/cradle press PROGRAM * # followed by the system password ( default is 1234). Now press 604 and then SP-PHONE. Enter the jack number you wish to change ( 01 is extension 101, 02 is extension 102 etc. ). Enter the name ( basically the same as texting on a cellphone ). Press AUTO DIAL / STORE to save your change. To go to the next extension press SP-PHONE. Don’t forget to press AUTO DIAL / STORE to save your change after each name entered. Press PROGRAM to exit program mode and you are done.
PLEASE rate / vote this answer if it was helpful.
Thank you.

The side buttons is programmed as extensions
To change the extension names follow these steps :

If you are using the KX-T7730 phone on a Panasonic KX-Txx 308 or 824 system.
From the Switchboard / Main telephone ( usually ext 101, 10 or 9 ) with the handset on the cradle/hook :
1. Press PROGRAM * # followed by the system password ( default is 1234).
2. Now press 604 and then SP-PHONE. Enter the jack number you wish to change ( 01 is extension 101, 02 is extension 102 etc. ).
3. Enter the name ( basically the same as texting on a cellphone ). Press AUTO DIAL / STORE to save your change.
4. To go to the next extension press SP-PHONE. Don’t forget to press AUTO DIAL / STORE to save your change after each name entered.
5. Press PROGRAM to exit program mode and you are done.

If you are using the KX-T7730 phone on a Panasonic KX-Txx 308 or 824 system. From the Switchboard / Main telephone ( usually ext 101, 10 or 9 ) with the handset on the cradle press PROGRAM * # followed by the system password ( default is 1234). Now press 604 and then SP-PHONE. Enter the jack number you wish to change ( 01 is extension 101, 02 is extension 102 etc. ). Enter the name ( basically the same as texting on a cellphone ). Press AUTO DIAL / STORE to save your change. To go to the next extension press SP-PHONE. Don’t forget to press AUTO DIAL / STORE to save your change after each name entered. Press PROGRAM to exit program mode and you are done.
PLEASE rate / vote this answer if it was helpful.
Thank you.

If you are using the KX-T7730 phone on a Panasonic KX-Txx 308 or 824 system.
From the Switchboard / Main telephone ( usually ext 101, 10 or 9 ) with the handset on the cradle/hook :
1. Press PROGRAM * # followed by the system password ( default is 1234).
2. Now press 604 and then SP-PHONE. Enter the jack number you wish to change ( 01 is extension 101, 02 is extension 102 etc. ).
3. Enter the name ( basically the same as texting on a cellphone ). Press AUTO DIAL / STORE to save your change.
4. To go to the next extension press SP-PHONE. Don’t forget to press AUTO DIAL / STORE to save your change after each name entered.
5. Press PROGRAM to exit program mode and you are done.