Thank you for holding on to me.
Here is an update so far.
I have start over with a fresh MoodleBox image and I connect the pi to my home network. In my home router, I bind the Pi's MAC address to 192.168.1.60 so I don't have to configure in /etc/dhcpcd.conf file. I also have configured my home network DNS configuration to the Pi (192.168.1.60), but still i couldn't access the Moodle website.
After some brainstorming with my colleagues, I manage to get access the website.
Let me explain the steps.
after reconsidering @Ratna 's advice. to add a DNS record, I have do homework on how to add a record in DNSMASQ.
Turns out, you can add records easily in /etc/hosts file, as the DNSMASQ will also look in the /etc/hosts file. So, I have add (in the /etc/hosts file)
Next, restart the dnsmasq.service.
sudo systemctl restart dnsmasq.service
***after this step, i still cannot access the Moodle website yet. but after i have add this line in /etc/dnsmasq.conf
Now, i can successfully access the Moodle website. I can access it using http://moodlebox.home, http://192.168.1.60 (will also redirect to http://moodlebox.home). without editing hosts file on my windows notebook.
BUT make sure to turn off DNS/VPN on your devices (windows, mac, iphone, android). because I personally configure my DNS to dns.adguard.com to block all the ads.
I am not sure why but if there are other DNS configured, I cannot access the Moodle website.
Thus, my issue is solved! Yey. Thank you @Nicolas, @Ratna, @krause