Good day,
I am an expert in elearning with over 18 years of experience that includes but not limited to Moodle development for over 12 years.
As you may know, upgrading version 2 to the latest one version 3.6.x will require the upgrade to be in 3-4 steps which means that it needs to be upgraded 3 times, each time upgraded and stabilized before upgrading the next step, the whole process is a cumbersome and relies mainly on the size of the Moodle instance, course sizes & number, plugins used if they are upgradable or alternatives if they aren't.
This is an approximate cost, to give you an accurate one, I need to have a look at your Moodle.
Kindly have a chat with me to discuss details.
Regards,