Here’s a regex using the pipe symbol as OR to allow only 6 possible values.

regex="efs-(00|04|08|12|16|20)00"

Matches:

efs-0000
efs-0400
efs-0800
efs-1200
efs-1600
efs-2000

No matches:

efs-0100
efs-2200
efs-0600
efs-1400
efs-1800
efs-1110
111022
asdb023
2330asd
1200-efs
1205
abc

$var is compared with $regex to find a match. $var is any of the variables above.

if [[ $var != $regex ]]; then
  echo "Not a match"
else
  echo "It's a match"
fi