I want to push this file to my cell phone I do adb shell

Then I do ls

~ $ ls -l
drwxr-xr-x    4 root     root          4096 Feb 14 08:54 cache
lrwxrwxrwx    1 root     root            13 Jan  1  1970 charger -&gt; /sbin/healthd
drwxrwxr-x    7 system   system        4096 Jan  2  2000 config
-rw-r--r--    1 root     root          2925 Jan  1  1970 config_init.sh
drwxrwx--x    4 root     root             0 Feb 14 09:57 data
drwxr-xr-x    2 root     root             0 Feb 14 09:57 datadata
-rw-r--r--    1 root     root          4350 Jan  1  1970 default.prop
drwxr-xr-x   12 root     root          3140 Feb 14 11:15 dev
-rw-r--r--    1 root     root          1320 Jan  1  1970 droidboot.init.mofd_v1.rc
drwxr-xr-x    2 root     root             0 Feb 14 09:57 emmc
drwxr-xr-x    2 root     root             0 Feb 14 09:57 etc
drwxr-xr-x    2 root     root             0 Feb 14 09:57 external_sd
drwxrwx---    7 system   system        4096 Nov 15 10:10 factory
-rw-r--r--    1 root     root         16565 Jan  1  1970 file_contexts
-rw-r--r--    1 root     root          1604 Jan  1  1970 fstab
-rw-r-----    1 root     root           595 Jan  1  1970 fstab.charger.mofd_v1
-rw-r-----    1 root     root           806 Jan  1  1970 fstab.mofd_v1
-rw-r-----    1 root     root           595 Jan  1  1970 fstab.ramconsole.mofd_v1
-rw-r-----    1 root     root           151 Jan  1  1970 fstab.zram
-rwxr-x---    1 root     root        653412 Jan  1  1970 init
-rwxr-x---    1 root     root          1938 Jan  1  1970 init.class_main.sh
-rwxr-x---    1 root     root           109 Jan  1  1970 init.firmware.rc
-rwxr-x---    1 root     root          5253 Jan  1  1970 init.rc
-rwxr-x---    1 root     root           436 Jan  1  1970 init.watchdog.rc
-rw-r--r--    1 root     root          1081 Jan  1  1970 intel_prop.cfg
drwxr-xr-x    3 root     root             0 Jan  1  1970 lib
lrwxrwxrwx    1 root     root            10 Feb 14 09:47 logs -&gt; /data/logs
drwxr-xr-x    2 root     root             0 Feb 14 09:57 mnt
-rw-r--r--    1 root     root          3220 Feb 14 09:56 original.fstab
dr-xr-xr-x  125 root     root             0 Feb 14 09:47 proc
-rw-r--r--    1 root     root          3070 Jan  1  1970 property_contexts
drwxr-xr-x    3 root     root             0 Feb 14 09:56 res
-rw-r--r--    1 root     root           240 Jan  1  1970 rfkill_bt.sh
drwx------    2 root     root             0 Jun 26  2015 root
drwxr-xr-x    2 root     shell            0 Feb 14 09:56 sbin
drwxr-xr-x    2 root     root             0 Feb 14 09:57 sd-ext
lrwxrwxrwx    1 root     root            11 Feb 14 09:57 sdcard -&gt; /data/media
-rw-r--r--    1 root     root           534 Jan  1  1970 seapp_contexts
-rw-r--r--    1 root     root            73 Jan  1  1970 selinux_version
-rw-r--r--    1 root     root        141154 Jan  1  1970 sepolicy
-rw-r--r--    1 root     root         10548 Jan  1  1970 service_contexts
dr-xr-xr-x   14 root     root             0 Feb 14 09:47 sys
drwxr-xr-x    5 root     root             0 Jan  1  1970 system
drwxr-xr-x    2 root     root             0 Feb 14 09:57 tmp
-rw-r--r--    1 root     root          3388 Jan  1  1970 ueventd.mofd_v1.rc
-rw-r--r--    1 root     root          4487 Jan  1  1970 ueventd.rc


Now there is a zip file that contains my cyanogenmod. However, I couldn't find in which directory it is.

It is on the external sd card.

So how can I push some files to the root directory of my external sd card?

I did 

cd /
ls -R *.zip


I got nothing even though I know that some zip files definitely exist

I did cd /external_sd

But the directory is empty
If you want to push your files inside sdcard. You need to push it inside /mnt/sdcard/. That is where your sdcard is mounted inside adb shell