First ... who is service provider? and what operating system?
Makes a difference ... share host or standalone ... Linux (which flavor) or Windows?
Service provider is correct ... it's more a 'march' through versions ... do not 'hyperjump' from 2.6 to 3.2.
Example: your first 'hop' is to 2.7.highest. There you will have to check themes, update assignments, and check Quiz Upgrade helper as well. If one doesn't take of those at this stage, some of the tools for upgrading parts/pieces disappear in future versions upwards.
Also ... check what is required to run each version ... what version of PHP ... what verson of MySQL.
Start with https://docs.moodle.org/26/en/Upgrading
https://docs.moodle.org/26/en/Upgrading
https://docs.moodle.org/27/en/Upgrading
https://docs.moodle.org/29/en/Upgrading
https://docs.moodle.org/30/en/Upgrading
https://docs.moodle.org/32/en/Upgrading
Easiest way to 'march' is git ... that is dependent upon the questions asked above.
https://docs.moodle.org/27/en/Git_for_Administrators
Uhhh .... I've 'marched' quite a few. :\
'spirit of sharing', Ken