The path to make.exe (as well as fpc and other tools used) is stored in the user config.
Default on Windows C:\Users\USERNAME\AppData\Local\lazarus
Default on linux ~/.lazarus
So, if you had Lazarus 1.0.6 or earlier before, then the path may still have pointed to 2.6.0, as those Versions came with 2.6.0
I am not sure, why the path was not upgraded. There may be a bug there...
Anyway, all you need to do is to go to Menu Tools > Options and change 2.6.0 to 2.6.2 in any of the path listed.
Or, you can, in the installer, check the option to delete your old config. But that deletes all your preferences, so I recommend to edit the path only.
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Also you may had other versions such as 1.0.14 (which has 2.6.2) installed after 1.0(.6).
They would have worked, if you installed, without uninstalling the old version. Because then both fpc would be present, as the old 2.6.0 is not overwritten.
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Lazarus 1.2.2 (to be released soon) upgrades fpc to 2.6.4
So if you upgrade, simply go to Menu Tools, Options, and look at the path for fpc, fpc source and make.
And make sure they contain 2.6.4