Relationship design for auto parts store database
You have all the tables you need and you have the many-to-many relationships correct, I think. 

I'd suggest that you add a Parent field to Category and then create a hierarchy of categories instead of having a Category table with a single Subcategory table.

create table Category(
    CategoryId int not null identity(1,1),
    ParentCategoryId int null,
    CategoryName nvarchar(100) not null,
    primary key (CategoryId))


As a point of style, I'd name the many-to-many tables with underscores instead of numbers, i.e. Model_Year_Part.

Note that I used nvarchar instead of varchar.

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