This should solve your problem.
Try a different usb cable. My cable was bad. Charging was ok but did not attach the phone.
driver Asus for Windows: http://www.asus.com/sa-en/support/Download/39/1/0/2/32/
Choose target device: USB device
Install Asus PC Link on your PC available here: https://www.asus.com/ph/support/FAQ/1007320/
This are the steps :
I haven't tried for eclipse but it might work for that also.
To enable USB Debugging first you need to enable Developer Options.
Open Zenfone Settings and scroll down and tap About.
Scroll down and select Software Information.
Under Software information you will see Build Number.
Tap Build Number 7 times to enable Developer Options.
Come back to Settings and scroll down to find Developer Options.
Tap on Developer Options and it will open upto give you option to enable USB Debugging
I had the same problem. I solved it the following way :
1. Go to Settings->Storage->Click the USB icon at top
2. Make sure that MTP is selected
Settings > Storage > Click the USB Icon at the upper right corner > Check your choice
Source: Stackoverflow.com