What's worse, too many entities or too many tables? I just had a question about database design, I am in fairly early learning stages of this so bear with me.

Suppose I have a parent table called "Projects" each "Project" Entity can have any number of "Attachments" and each "Attachment" can have any number of "Anchors".

I can only see a few possible solutions for this.
Estimations assume 10 years use of this database:
300 Projects/year * 3 Attachments/Project * 20 Anchors/Attachment

Solution 1 (My initial design idea):

Involves 3 tables. "Projects"->"Attachments"->"Anchors"

Number of Tables: 3

Max entities in a table: 180,000 in "Anchors"

Solution 2:

Involves 2+n tables.  "Projects"->"Attachments"->"Anchors[n]"

Number of Tables: 9,002 (9,000 Anchor Tables)

Max entities in a table: 9,000 (In Attachment Tables)

Solution 3:

Involves 1+n1+n2 tables. "Projects"->"Attachments[n1]"->"Anchors[n2]"

Number of Tables: 12,001 (3,000 Attachment + 9,000 Anchor)

Max entities in a table: 3,000 (In Project Tables)

To summarize:

What's worse, more entities or more tables?
AND/OR
Is there simply a better design for this situation that I am unaware of?
The number of entities is driven by the functional specs on the database.  You discover entities by analyzing the subject matter.  This is different from inventing entities because it feels good.  You determine whether any given subject matter entity is relevant to the database by looking at the scope of the database, per the requirements.

The number of tables is driven by the database design.  You create tables as needed to fulfill the design goals.  You are typically pursuing multiple goals:  normalization, simplicity, flexibility, and speed, among others.  Typically each entity will have a table of its own, and there will be extra tables for relationships that are not simple enough to just add FKs to existing tables.

The difference between analysis and design is crucial to all projects beyond simple exercises.