This should do the trick:

-- note how this starts off by creating a table structure and putting data into it?

-- In order to get people willing to help, this is a prerequisite on your part.

-- see the link in my signature for how to do this.

declare @VerizonDetails table ([Connect Time2] TIME, [totalTime2] TIME)

insert into @VerizonDetails

values ('08:05:44.0000000', '00:13:00.0000000'),

('08:05:57.0000000', '00:01:00.0000000'),

('09:07:42.0000000', '00:03:00.0000000'),

('09:07:46.0000000', '00:09:00.0000000'),

('09:08:08.0000000', '00:01:00.0000000')

-- add the two times together, first converting them to datetimes

select *, convert(time, CONVERT(datetime, [Connect Time2]) + CONVERT(datetime, totalTime2))

from @VerizonDetails