Can i pair multivalued attribute with an entity? If i have the following scenario.


  Every doctor can diagnose a disease for different patients. A diagnose
  holds a date and disease(multi valued attribute). So the patient has
  testing that need to be done with investigation, the investigation
  holds type, description and title and testing holds date. For each
  investigation we know the disease that need to be investigated, hence
  one disease can have multiple investigations.


This is the sentence where i have difficulties


  For each investigation we know the disease that need to be investigated, hence one disease can have multiple investigations.


I have the following diagram so far. My question is can i connect multivalued disease with Investigation entity? I am new to EER diagrams
Yes, you can. 

You could create a table for Diseases:

TABLE disease
-------------
disease.id (PK)
disease.name 


Then you can model Diagnosis (note that's a junction table) this way:

TABLE diagnosis
---------------
diagnosis.id (PK)
diagnosis.date
diagnosis.doctor_id (FK)
diagnosis.patient_id (FK)
diagnosis.disease_id (FK)


So you can add a Disease to an Investigation:

TABLE investigation
-------------------
investigation.id (PK)
investigation.type
investigation.title
investigation.description
investigation.disease_id (FK) 


And finally, here's the table for Testing:

TABLE testing
-------------
testing.id (PK)
testing.date
testing.investigation_id (FK)
testing.patient_id (FK)


The Testing can as well be included as a field in Investigation instead of having its own table, unless the exercise requires it.

Then there are the tables for Doctor and Patient which you already modeled.

This is the description of the tables, from it you can easily create the ER diagram, remembering that a FK on a table connects to the PK on another table.