cur=$(date +%m) # Need not be described

next6=$(printf %02d $(echo $(($cur+6))%12 | bc))
# 1. $(($cur+6)) is same 'expr' command. result is 7
# 2. echo 7%12 | bc  result '7' (remainder)
# 3. printf %02d => 01, 02, 03 ... 
# 4. $next6 => current month + 6
# 5. My mistake, if $next6 is 0 => change 1  (if [ $next6 == 0 ];then next6=1;fi)
# 6. END

next6_y=$(echo $(($cur+6))/12 + $(date +%Y) | bc)
# 1. $(($cur+6)) is same 'expr' command. result is 7
# 2. echo 7/12 | bc  result '0' (quotient)
# 3. $(date +%Y) ==> 2016
# 4. 0 + 2016 | bc  ==> 2016
# 5. END