I did go to Auto Zone and they gave me the diagnosis error code is (PO2631)but they don't know what is it means.

That is because that number is WRONG
P0xxx is the format , yours is too long. P0 p1, OR P2.
use any modern, scan tool, to read the codes.
be sure to write them down more carefully.
ok i see your error, you added a 0 . (i think i got it)
there is no zero, P2 codes are factory codes.
p0 is federal codes,
and autozoned, is clueless to them, they;'d need and fsm on every car made to decode all P2 codes on all cars. a hopeless path.

why not just look them up in authoritative sources
like, SUZUKI or Alldata.com and avoid the ZONED.
answer, USA answers 06 GV
2631 is the oxygen sensor, failure,(or its wires damage, in all cases)
V6 engine code, 2.7Liter
bank 2, sensor one.
decoding that , bank 2 is the bank not on cylinder 1 side.
the right bank is bank2
its the top right (upstream) sensor is bad.
http://www.fixkick.com/sensors/O2%20sensor/25L/25L-O2-H3LL.html

right means from drivers perspective.

best path is here
the price 4 bucks
the book is here
https://suzukipitstopplus.com/Products/1045-2006-grand-vitara-service-manual.aspx

the FSM has your answer.

Front
B1 -B2
1 -- 2
3 -- 4
5 -- 6

bank 1 is left, bank 2 is right. per below, on all v6 by Suzuki