I want to buy a raspberry-pi 4 and for some reasons i need to install an old linux kernel on it (for example raspbian with linux kernel 4.14) I want to know that can i install old raspbian images on raspberry-pi 4 board (because raspberry-pi 4 is new board i think that maybe i can not install old raspbian images on it)??
Yes, it is possible to run Stretch on a Pi 4.
The easiest way is to run Stretch in a virtual machine within Buster.
And I have released a bootable image to do exactly that. Just flash it to an SD card, then boot it, then click the menu item I added:
A terminal window will open with a full Stretch CLI. After you enter the username (pi) and password (raspberry), the graphical interface for Stretch will open in a VNC-style window.
There are some who claim to have Stretch on a Pi4, and it is at least theoretically possible, as Stretch is now updated to the same kernel version (4.19.66) as Buster.
HOWEVER the Pi4 firmware, boot code and the Pi4 version of the kernel is not included in Stretch, so would have to be manually installed.
There is no (simple) way you could use kernel 4.14, unless you were prepared to make a custom version, but it is difficult to think of any reason why you could not use the newer kernel or why you would need an older version.
Is it worth it - NO There is a reason the Foundation used Buster for the Pi4 before its official release - because it is a massive job.