You can open the terminal by typing terminal in the app menu to search it, or the more easy way, just press the ctrl+alt+t keys at the same time.
Once terminal is open, enter into it:
soffice -writer
For options, you can enter:
soffice -?
Alternatively, you can press alt+F2 to pull up the Launcher and enter soffice -writer into that and hit enter or the Launch button.
Yes, Zorin OS comes with LibreOffice, not Open Office. Libreoffice launches with:
libreoffice --writer
Actually this command opens LibreOfiice Write on my system.
So do you think that the OP confused LibreOffice with OnlyOffice?
I dunno... maybe... Just covering the bases...
I had no idea that soffice -writer will open libreoffice --writer. How interesting.
Yes, soffice -writer opens Libre. So, that does not get me to Only Office.
Someone did install Zorin for me. Only Office is in the Zorin apps.
On a sidenote, you may need JRE:
sudo sudo apt install openjdk-8-jre
Thanks for this info.
So you have no idea how this OnlyOffice has been installed?
Is it not for OpenOffice?
OP's question is about OnlyOffice
If not, please open the Software store from the app menu: software
Click the Installed button at the top.
It is in alphabetical order - scroll down and search for Open Office.
Click on the entry and scroll down the page to check Source.
From what I understand, Open Office needs java runtime environment...
EDIT Only office. Not open office. See how long I have been on the forum troubleshooting? I am getting brainless and illiterate.
This is what happens...
I never even heard of onlyoffice...
I understand it.
But OP is NOT asking about OpenOffice.
He is asking about OnlyOffice.
Those are two different apps.
I bet it is a Snap. 
I used it a short while when I was using Peppermint OS.
Peppermint has a very slick desktop integration for such web apps.
Not necessary so.
When you search for OnlyOffice in Software, the first one showing is Flatpak.
(That was the starting point of our Flatpak ordeal BTW.)
I downloaded a DEB file for Only Office and tried to install it. That is probably how it ended up in the apps list.
Thanks for this additional info.
This would certainly help our detective work.
While you trying to install this deb file, did you get any error message?
Also, please let us know the version of your Zorin.
Zorin 15.3 or 16 beta / Core/Lite/Ultimate
No, nothing seems to happen.
I think I have Zorin 15,3 Core.
Did you download the .deb file?
Is it still in your ~/Downloads folder?
If so, you can double click it to open it in the Gdebi Installer. It will have two buttons on the upper right side- Reinstall or Remove.
I think OP has to install Gdebi first.
I do not remember it comes with Zorin.
sudo apt install gdebi
If OP lost the installer it is here:
Ok, corrected version:
Did you download the .deb file?
Is it still in your ~/Downloads folder?
If so, you can double click it to open it in the Installer. It will have two buttons on the upper right side- Reinstall or Remove.