Can someone please tell me where I went wrong for an exercise submission

Good. The essentials are there. A first rough list of entities is to take the nouns of the story - office, employee, project, clients, assignment, skill. Each table has a unique, sequential, meaningless key. Columns are given descriptive names. Here are the suggestions by entity.

office> The manager is an employee and should have a separate foreign key relationship with manager_employee_id. There is a many-to-many with employee. Avoid M-to-M relationships. In this case, an office has many employees. But an employee has one home office. I suggest naming fields uniquely with a common suffix describing the domain, office_address, instead of address.

employee> The job_id should be a foreign key to job instead of title. The office_id should be a foreign key to office instead of location. The column names should be hire_date instead of the start_date to avoid confusion with the project start_date. Use employee_address instead of address based on the domain suffix rule.

project> The project manager is a separate foreign key to employee pm_employee_id. What is the business difference between estimated_cost and quoted_cost? Make sure there is a foreign key field to match every relationship line. Client_id should be the foreign key. Office_id should be a foreign key.

assignment> Good, this is an intersecting table between project and employee. I suggest renaming the date to assigned_date to keep the suffix consistent. Notice that the hours_worked are in this table with the assigned_date. The assigned_date happens once. But the hours worked happen daily.

daily_assignment> Maybe there should be a separate child table called daily_assignment with its own primary key, a foreign key to assignment, and the worked_date and hours_worked as fields. This tracks each item of data uniquely at its own level.

client> I suggest renaming the address to client_address.

There are ways to make it more complicated. But I think this model works well. It should give you flexibility to make business changes, yet still be simple enough to code.

There are basically just two things here:

1. Your data model, which is the structure of your entities, attributes and relationships.

2. The graphical representation of your data model.

Your data model may be high level (entities/relationships only) or lower level (add in attributes with details of data types) and it may be logical or physical. It all depends on what stage of your design process you're at. The point of a data model is to record your database design, which is just an expression of your business requirements for persisting data.

Crows foot and ERD etc. are just graphical conventions for showing your data model pictorially. The great thing about standards is that there's so many to choose from, and this is also true of graphical conventions. Read this wiki article for a sampling.

Which conventions you choose may depend on what you need to communicate about your model, or it might just depend on what conventions make sense to you.

Don't get too wound up about all the different terminology. It's all just your database design and how you choose to record and communicate it.