This video goes through in detail how to upgrade your Samsung Galaxy Note 3 from Jelly Bean 4.3 to KitKat 4.4.2 manually using Odin. In this case i am using a Chinese Variant SM-N9006 Snapdragon 800.
odin: https://odindownload.com/
SamMobile: https://www.sammobile.com/firmwares/
Videos in this Series – Samsung Galaxy
JellyBean
I9000 – Install CWM & Jelly Bean onto your Galaxy S
Note 3 JB – Root Using UDLV Method
KitKat
Note 3 KK – Install CWM and Gapps On Your Note 3
Note 3 KK – Root using CF-Auto-Root and Install TWRP
Note 3 KK – Upgrade Your Galaxy Note 3 using Odin
LolliPop
Note 3 LP – Upgrade Your Galaxy Note 3 using Odin