The giants referred to in Bere’shiyth, and described with more particularity in the cepher Chanoch (book of Enoch), Yovheliym (book of Jubilees), and referenced in Kepha Sheniy (2 Peter) and Yahudah (Jude), are those giants that were present before the flood, in the antediluvian period.

Yovheliym (Jubilees) 7:20-25

And in the twenty eighth jubilee Noach began to enjoin upon his son’s sons the ordinances and commandments, and all the judgments that he knew, and he exhorted his sons to observe righteousness, and to cover the shame of their flesh, and to bless their Creator, and honour father and mother, and love their neighbour, and guard their souls from fornication and un-cleanness and all iniquity.

Here we see that the Torah was understood by Noach well before it was given to Mosheh.  This understanding, whether written or oral, was carried forward by the sons of Noach and their sons, or so it says in this passage.

Yovheliym (Jubilees) 7:21-25

21 For owing to these three things came the flood upon the earth, namely, owing to the fornication wherein the Watchers against the Torah of their ordinances went a whoring after the daughters of men, and took themselves women of all which they chose: and they made the beginning of uncleanness. 22 And they begat sons the Nephiliym, and they were all unlike, and they devoured one another: and the Giants slew the Nephiyl, and the Nephiyl slew the Elyo, and the Elyo mankind, and one man another. 23 And everyone sold himself to work iniquity and to shed much blood, and the earth was filled with iniquity. 24 And after this they sinned against the beasts and birds, and all that moves and walks on the earth: and much blood was shed on the earth, and every imagination and desire of men imagined vanity and evil continually. 25 And YAHUAH destroyed everything from off the face of the earth; because of the wickedness of their deeds, and because of the blood which they had shed in the midst of the earth he destroyed everything.

Shemu’el Sheniy (2 Samuel) 21:15-22

Moreover the Pelishtiym had yet war again with את eth-Yisra’el; and David went down, and his servants with him, and fought against את eth-the Pelishtiym: and David waxed faint. 16 And Yishvu VeNov, which was of the sons of the Repha’iy, the weight of whose spear weighed three hundred sheqels of brass in weight, he being girded with a new sword, thought to have slain את eth-David. 17 But Aviyshai the son of Tseruyah helped him, and smote את eth-the Pelishtiy, and killed him. Then the men of David swore unto him, saying, You shall go no more out with us to battle, that you quench not את eth-the light of Yisra’el. 18 And it came to pass after this, that there was again a battle with the Pelishtiym at Gov: then Cibbekay the Chushathiy slew את eth-Caph,  which was of the sons of the Repha’iy. 19 And there was again a battle in Gov with the Pelishtiym, where Elchanan the son of Ya`arey Oregiym, a Beyt Hal-Lachmiy, slew את eth the brother of Golyath the Gittiy, the staff of whose spear was like a weaver's beam. 20 And there was yet a battle in Gath, where was a man of great stature, that had on every hand six fingers, and on every foot six toes, four and twenty in number; and he also was born to the Repha’iy. 21 And when he defied את eth-Yisra’el, Yahunathan the son of Shim`iy the brother of David slew him. 22 את eth-These four were born to the Repha’iy in Gath, and fell by the hand of David, and by the hand of his servants.

There were four Repha’iym found in this passage: Yishvu VeNov, Caph, the brother of Golyath, and the man with great stature.  Rather than discuss the size of these giants in terms of cubits, here we get descriptions. Yishvu VeNov carried a spear that weighed 300 hundred sheqels of brass. The brother of Golyath carried a spear that was like a weaver’s beam.  In short, they are described as giants, and conspicuously, one of them had 12 fingers and 12 toes.

Ezra, in his first book of Chronicles, relates the same story:

Divrei Hayamiym Rishon (1 Chronicles) 20:4-8

And it came to pass after this, that there arose war at Gezer with the Pelishtiym; at which time Cibbekay the Chushathiy slew את eth-Cippay, that was of the children of the Repha’iy: and they were subdued. 5 And there was war again with את eth-the Pelishtiym; and Elchanan the son of Ya’iyr slew את eth-Lachmiy  the brother of Golyath the Gittiy, whose spear staff was like a weaver's beam. 6 And yet again there was war at Gath, where was a man of great stature, whose fingers and toes were four and twenty, six on each hand, and six on each foot: and he also was the son of the Repha’iy. 7 But when he defied את eth-Yisra’el, Yahunathan the son of Shim`a David’s brother slew him. 8 These were born unto the Repha’iy in Gath; and they fell by the hand of David, and by the hand of his servants.

We discover that the brother of Golyath is named Lachmiy, and the man of great stature is again identified that he had six fingers on either hand, and six toes on either foot.  Here, therefore, is the second witness.

For further reading...

The Giants - Part 1

The Giants - Part 3

The Giants - Part 4

The Souls of the Giants - Part 5