You mustn't use spaces around =, so it should look like this:
PATH=$PATH:/google_appengine
To Answer the question
The answers and some comments focus on how to set JAVA_HOME to version 11 but the question is partly about "where is version 8 being set?". To answer that see:
Use this command:
$ sudo grep -rnw --exclude-dir={boot,dev,lib,media,mnt,proc,root,run,sys,/tmp,tmpfs,var} '/' -e '/usr/lib/jvm/java-8-oracle' | grep JAVA_HOME
/etc/profile.d/jdk.sh:4:export JAVA_HOME=/usr/lib/jvm/java-8-oracle
/etc/profile.d/jdk.csh:4:setenv JAVA_HOME /usr/lib/jvm/java-8-oracle
/home/rick/.gradle/daemon/4.6/daemon-14831.out.log:53:20:45:23.553 [DEBUG] (... SNIP ...) /usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin:/usr/games:/usr/local/games:/snap/bin:/usr/lib/jvm/java-8-oracle/bin:/usr/lib/jvm/java-8-oracle/db/bin:/usr/lib/jvm/java-8-oracle/jre/bin (... SNIP ...) Configuring env variables: {PATH=/home/rick/bin:/home/rick/.local/bin:/mnt/e/bin:/mnt/e/usr/local/bin:/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin:/usr/games:/usr/local/games:/snap/bin:/usr/lib/jvm/java-8-oracle/bin:/usr/lib/jvm/java-8-oracle/db/bin:/usr/lib/jvm/java-8-oracle/jre/bin, (... SNIP ...)
This is what my system returns. Yours will likely be different. To make a long story short the culprit is /etc/profile.d/jdk.sh:
$ cat /etc/profile.d/jdk.sh
setenv J2SDKDIR /usr/lib/jvm/java-8-oracle
setenv J2REDIR /usr/lib/jvm/java-8-oracle/jre
setenv PATH ${PATH}:/usr/lib/jvm/java-8-oracle/bin:/usr/lib/jvm/java-8-oracle/db/bin:/usr/lib/jvm/java-8-oracle/jre/bin
setenv JAVA_HOME /usr/lib/jvm/java-8-oracle
setenv DERBY_HOME /usr/lib/jvm/java-8-oracle/db
You probably surmise /etc/profile.d/jdk.csh needs changing too. Indeed it contains the exact same contents as /etc/profile.d/jdk.sh
To address the XY problem
There is a better way than going through files line by line and changing an 8 to an 11.
The easiest method is using Java installer. From this Ask Ubuntu Q&A: Setting JDK 7 as default
To get a list of your installed Java platforms, run the following command from the terminal:
sudo update-alternatives --config java
This will give you a list output similar to this:
There are 2 choices for the alternative java (providing /usr/bin/java).
Selection Path Priority Status
------------------------------------------------------------
0 /usr/lib/jvm/java-6-oracle/jre/bin/java 1070 auto mode
1 /usr/lib/jvm/java-7-openjdk-i386/jre/bin/java 1051 manual mode
* 2 /usr/lib/jvm/java-6-openjdk-i386/jre/bin/java 1069 manual mode
Press enter to keep the current choice[*], or type selection number:
Best Answer
Finally figured it out. For SOME reason, the go folder in
/usr/localwas not executable. Changed the file permissions, and it's working now. Leaving this question here in case someone else finds this useful.