If the utility program, such as a printer utility program, is running, exit the program or temporarily disable it.

If you cannot select Hibernate mode, click Change advanced power settings and check if Allow hybrid sleep under Sleep is set to Off. If it is set to On, change it to Off. See Selecting a Power Plan to change the power plan settings.

Your VAIO computer may not enter Hibernate mode if you execute a task on the computer before the computer completely enters Hibernate mode.