How can I put the employer's social security if only the last 4 social security numbers appear in my w-2?

You have to get the physical paper W-2 from your employer.  Or ask your employer for their nine digit EIN.

Your employer should be using an EIN.   Or if for some odd reason they are using their SSN, they need to provide the entire SSN to you.  Ask the employer.

If you got a W2 from him they have to use a 9 digit EIN like xx-xxxxxxx.  They can't use a social security number on a W2 except for your ssn.   Did you maybe get a 1099NEC instead of a W2?    

Box "b" the employer tax number, can't be hidden on your official W-2.  Contact your employer.  (And, they can't be using their personal SSN if they have employees, even if they are a small business.  They must get an EIN employer ID number from the IRS.)

On the other hand, your SSN in box "a" could be partially hidden, but you should know your own SSN.