Bookrack.rb
has_many :faculties

Faculty.rb
belongs_to :bookrack
has_many :books

Book.rb
belongs_to :faculty
has_many :barcodes

Barcode.rb
belongs_to :book

has_many :faculties
has_many :books, through: :faculties
has_many :barcodes, through: :books

Bookrack.find(1).barcodes.count

b = Bookrack.first.faculties.first.books.first.barcodes.count

# app/models/bookrack.rb
has_many :faculties

# app/models/faculty.rb
belongs_to :bookrack
has_many :books

# app/models/book.rb
belongs_to :faculty
has_many :barcodes

# app/models/barcode.rb
belongs_to :book

Bookrack.joins(faculties: [books: :barcodes]).count
# => SELECT COUNT(*) FROM "bookracks"
#    INNER JOIN "faculties" ON "faculties"."bookrack_id" = "bookracks"."id"
#    INNER JOIN "books" ON "books"."faculty_id" = "faculties"."id"
#    INNER JOIN "barcodes" ON "barcodes"."book_id" = "books"."id"
# => 1