In the screenshot below, I am trying to extract the Order Number that starts with "300"...In other words, if I see a "300", I want to extract 8 characters starting with "300".  Any suggestions?

=if(left(Name,6)="---300",mid(Name,4,8),"")

Can you do a search formula? = If(SEARCH("300",Name,1)>0,Name,"")

Correction - this may work better:

=mid(Name,search("---300",Name)+3,8)

I agree with Dawn, you can use a SEARCH formula to locate "300" in the string.   I used a  couple of formulas to solve a similar issue.

The first formula below looks for "REQ" in the field Req_Name and returns a number indicating what position the string begins in the field.  The second formula pulls in the 10 characters where "REQ" begins and if it doesn't locate the string the field will be blank. Hope this helps.

=Search("REQ",Req_Name)

=If(StrPosREQ>0,Mid(Req_Name,StrPosREQ,10),""

@Julie Whitehurst this worked perfect... thank you.