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find + awk approach for your current folder structure /home/myuser/parent1/<folder>:

find /home/myuser/parent1 -type f -name "*.png" \
     | awk -F'/' '{ a[$5]++ }END{ for(i in a) print i,a[i] }'

• $5 - points to a folder name at the needed level

find + awk approach for your current folder structure /home/myuser/parent1/<folder>:

find /home/myuser/parent1 -type f -name "*.png" \
     | awk -F'/' '{ a[$5]++ }END{ for(i in a) print i,a[i] }'

• $5 - points to a folder name at the needed level (adjust this if your folder structure is different; it should be two more than directory depth of the parent. (So for /tmp/parent1 it'd be $4, and for /home/myuser/Documents/parent1 it'd be $6).

find + awk approach:

find /home/myuser/parent1 -type f -name "*.png" \
     | awk -F'/' '{ a[$5]++ }END{ for(i in a) print i,a[i] }'

• $5 - points to a folder name at the needed level

find + awk approach for your current folder structure /home/myuser/parent1/<folder>:

find /home/myuser/parent1 -type f -name "*.png" \
     | awk -F'/' '{ a[$5]++ }END{ for(i in a) print i,a[i] }'

• $5 - points to a folder name at the needed level

find + awk approach:

find /home/myuser/parent -type f -name "*.png" \
     | awk -F'/' '{ a[$5]++ }END{ for(i in a) print i,a[i] }'

• $5 - points to a folder name at the needed level

find + awk approach:

find /home/myuser/parent1 -type f -name "*.png" \
     | awk -F'/' '{ a[$5]++ }END{ for(i in a) print i,a[i] }'

• $5 - points to a folder name at the needed level