Some words about the errors you get which hopefully will save you from similar situations in future.
In Linux ports from 0 to 1024 are reserved for system use. This means that in order to use one, you must have the authority to change - access basic system settings. The root user has such privileges and can actually use a port from the range 0 - 1024.
In your problem as you can see, the system through Apache2 response indicates the root of the problem ([...]could not bind to address blah blah 80):
(13)Permission denied: make_sock: could not bind to address [::]:80
(13)Permission denied: make_sock: could not bind to address 0.0.0.0:80
When the Apache2 http daemon starts, it tries to bind the 80 port as it is the default port for use in HTTP see, which is a port within the system assigned ports and as such it can only be accessed by root.
You executed the start command as a typical user without root privileges and led to failure to do so.
In simple words:
You:
Hi Apache2. I am Kongthap and I am telling you to start (/etc/init.d/apache2 start)
Apache2:
OK. I am starting (Starting web server apache2)
System, please give me port 80 to use and listen for connections.
System:
OK. One moment to check...
Ahh... Sorry Apache2 but I cannot let you run at 80 port, it is for personal use.
And you do not have the correct privileges to bind it. (Operation not permitted)
Apache2:
Ohh, Kongthap I failed to start, the System did not let me do it ((13)Permission denied:[...])
Conclusion
There are mainly two solutions to this problem:
Run the Apache2 HTTP daemon with root privileges using sudo:
sudo service apache2 start
or:
sudo /etc/init.d/apache2 start
Change the default port from 80 to something greater than 1024, say 2000, 2500, 9000, etc. A typical port to run when in such situation is 8080
sudo vi /etc/apache2/ports.conf
look for or if not there add:
Listen 8080
or any other port of your choice such as port > 1024 and the selected port is not used by another process.