How to Interpret John 19:14a and John 13:1a?

Mark’s Gospel says it was the third hour (9 am according to Jewish time) when Christ was crucified (Mark 15:25). John’s Gospel mentions the sixth hour
(12 am according to Jewish time) (John 19:14a).

Both Gospel writers are correct in their claims. Each Gospel writer uses different
time systems: Mark’s Gospel follows the Jewish time system while John
follows the Roman time system. The Jewish 24-hour period began in the evening at 6 pm and the morning of that day began at 6 am. According to Roman time,
the day extended from midnight to midnight as it does for us in our time.

Mark 15:25 clearly states that Christ was crucified at the third hour Jewish time which was around 9 am. "And it was the third hour when they crucified him."

John 19:14a says: "Now it was the day of Preparation of the Passover.
It was about the sixth hour." This occurred at 6 am according to Roman time. 

John describes the trial before Pilate as occurring around 6 o'clock in the morning. This event can have occurred some time between 6 am and 7 am.

Using Roman time is consistent with other references to time in John’s Gospel: 

John tells us that Jesus was tired from his journey from Judea to Samaria at the sixth hour (John 4:6) and asked the woman at the well for water. Given the length of his journey, his fatigue, and the normal evening time when people would come
to the well to drink and water their animals, this fits well with 6 pm according to Roman time. It's the end of a working day. Jesus is tired from his long journey;
the disciples have gone to find food; and the woman is drawing water
in connection with the evening meal.

John's reference to the tenth hour (John 1:39) would be 10 am according to Roman time. Two of John the Baptist's disciples went with Jesus, saw where
he was staying, and spent that day with him. This was about the tenth hour.
They stayed with Jesus from 10 am the whole day.

John's reference to the seventh hour (yesterday at the seventh hour, John 4:52) would be yesterday at 7 pm according to Roman time. The hours of darkness and the difficulties of a mountain path may well have prohibited movement till the next day. At first light, he hastens home and meets his servants with the happy news
of his boy's recovery. The words "yesterday at 7 pm" are then easily explicable.

John 13:1a ("Now before the Feast of the Passover") was, using Jewish counting,
in the evening just after sunset (6 PM) at the beginning of the day of Passover,

which was the day before the "Feast of the Unleavened Bread". But since John used Roman counting it was before the Passover. See also the chapters Passover and
Preparation of the Passover Lamb in Jesus' Last Days before his Crucifixion.

We can't know why John, as a Jew, accepted in his Gospel a form of counting hours that came outside Jewish way of counting and instead used Roman counting. But we can safely say that accepting the Roman way of counting time in John’s Gospel
provides an adequate and better understanding of certain biblical accounts;
it provides a good explanation of what are otherwise troubling differences between John’s Gospel and the Synoptic Gospels (Matthew, Mark, and Luke).

See also Critical verses in the gospels at the end of The Four Gospels.