My ford focus 2008 tyre.During the check up he said that the tyre is ok.i think it  needs to be changed.Thoughts  ?  https://ibb.co/kqP3RbK

It's very odd that you would even ask the question. As for who did the "check" of your 2008 focus, I can only assume were blind or stupid.

Yes you need a new tyre.

 

It's not through to the cords and not bulging so would pass MOT.  Definitely worth keeping an eye on though as a pinch like that has probably weakened the internal structure

MOT failure ?

Having just checked about 8 different sites on the matter it seems that any damage to the sidewall of a tyre in an automatic failure, there is no need for the sidewall to be bulging or for cords to be exposed (as there is for the main tread area).

Nearly all sites I've looked at have wording similar to this:-

Another common cause of MOT tyre fails is cuts, nicks, bulges and bubbles on the tyre sidewalls. Your sidewalls are vital to driver safety, since they absorb all the pressure that is exerted on your tyres. Any damage to your tyre sidewalls puts you at risk of a blowout. If your tyres are found to have any sidewall  damage, your vehicle will fail its MOT. 

When assessing cuts in a tyre, it is permissible to check whether a cut is deep enough to reach the ply or cord by using a blunt instrument to open the cut taking care not to cause further damage.

The following criteria should be used when assessing a cut in a tyre:

• any ply or cord that can be seen without touching the tyre - fail
• if by folding back rubber or opening a cut with a blunt instrument, so as not to cause further damage, exposed ply or cord can be seen irrespective of the size of the cut - fail
• if a cut which is more than 25mm or 10% of the section width whichever is the greater, is opened with a blunt instrument and cords can be felt but not seen - fail

Before failing a cut, you must make sure it’s the cords that you can feel not a foreign object. If you’re not sure, then you should pass and advise.

 

d) A tyre: (i) with a cut in excess of the requirements deep enough to reach the ply or cords (ii) with a lump, bulge or tear caused by separation or partial failure of its structure, including any lifting of the tread rubber or with cords exposed or damaged

Major Dangerous

Had the same experience. The cut in the sidewall is pretty deep but no sign of ply cord damage. I still replaced them with new bf goodrich tires just for peace of mind.