You can write the code either in the change event of the dropdown or in the Exit event of the dropdown.
If you use the change event use the below syntax..
if(xfa.event.newText =="Other")
fieldName.presence = "visible";
If you are using the exit event use the below syntax..
if(this.rawValue =="Other")
fieldName.presence = "visible";
Sample file is at the below location..
https://acrobat.com/#d=QZS2WmRlvgjTIePj8a6mkQ
Thanks
Srini