I have running Bugzilla 3.6.1 in Debian and i want to upgarde to 4.4.x

So installed new OS redhat and and copied all the contents and import database from oldserver its working for 3.6.1 and so tried to upgarde to bugzilla 4.4.x below is steps i used

Downloaded the latest bugzilla 4.4.8 and extracted in /var/www/html directory
Moved old bugzilla directory to bugzilla.old
copied from old bugzilla localconfig* to new
Copied data directory from old bugzilla to new
And started to run ./checksetup.pl but i am getting below error

DBD::mysql::db do failed: Can't create table 'bugs.#sql-7a3e_2e' (errno: 121) [for Statement "ALTER TABLE attach_data ADD CONSTRAINT fk_attach_data_id_attachments_attach_id FOREIGN KEY (id) REFERENCES attachments(attach_id) ON UPDATE CASCADE ON DELETE CASCADE"] at Bugzilla/DB.pm line 638. Bugzilla:B::bz_add_fks(Bugzilla:B::Mysql=HASH(0x5068ec8), "attach_data", HASH(0x49cab88), HASH(0x9578680)) called at Bugzilla/DB.pm line 542 Bugzilla:B::bz_setup_foreign_keys(Bugzilla:B::Mysql=HASH(0x5068ec8)) called at Bugzilla/Install/DB.pm line 722 Bugzilla::Install:B::update_table_definitions(HASH(0x2290570)) called at ./checksetup.pl line 170

You're mysql installation looks like it's...
1: Not installed
2: Not configured <- Although it's equally possible that the DB is properly configured but the new bugzilla install is not.
3: Not compliant

Checking to see if it's installed is normally pretty straight forward, post back if you need assistance.
Checking to see if it's configured correctly is pretty easy as well, assuming you have the original configuration file from your debian instance. (If the old bugzilla has cfg files then validating the bugzilla config should be relatively trivial as well)
Checking to see if it's compliant can be accomplished by discerning the mysql version ("mysql -V" will give you that in Slackware-Current).
Hope that helps

1: Not installed

Its installed

Mysql -v

Server version: 5.1.61 Source distribution

service mysqld status
mysqld (pid 31294) is running...

2: Not configured <- Although it's equally possible that the DB is properly configured but the new bugzilla install is not.

Created a database and user 'bugs' and given full access to bugs user

and also imported old data like below

mysql -u bugs -p bugs < /root/backup-02-23-2015-19-00.sql (This import is worked when installed it on redhat os and bugzilla 3.6.1 )

3: Not compliant

I did't understand

I'm sorry, I didn't mean to be obtuse. I was referring to dependencies. I singled out the Mysql install because that's the error log you showed me but any failed dependency could cause similar errors in the database.

From the buzilla release notes for upgrades from version 3.x to version 4.x...
There's lots and lots of dependencies for bugzilla, that's just a sampling. Reference the page I'm linking to.
When I upgrade stuff, I try to do it 1 or 2 point versions at a time and insure the dependencies are satisfied and I have critical functionality on each step before moving on to the next. Full version upgrades like you're doing (3.x -> 4.x) are particularly problematic.