Cannot See 'Task type' Field In Page Layout After Creating a New Task in Salesforce

Task Type field is set to Hidden by default. To change this, follow the steps below:

In Lightning Experience

1. Click on Gear icon | Setup | Object Manager
2. Enter Task on the 'Quick Find' box.
3. On the left panel, click Fields & Relationships.
4. Click Type field label  
5. Click Set Field-Level Security.
6. Set visibility to your preference and click Save.
7. On the left panel, click Page Layouts.
8. Click Task Layout and include 'Type' field in page layout.
9. Click Save.

In Salesforce Classic

1. Click on Setup | Build | Customize | Activities | Task Fields
2. Click Type.
3. Click Set Field-Level Security.
4. Set visibility to your preference and click Save.
5. On the left panel, click Task Page Layouts.
6. Edit Task Layout and make sure 'Type' is included in your current layout.
7. Save changes.
    

Note: We can also set field-level security for the field using the following steps: 

• Setup > Security Controls > Field Accessibility
• Task > View By Fields > on the Field drop-down, look for Type
• Set the permission by profile