1. **State the problem:** Simplify the expression $$B = 3 \cos^2 x \times (1 - 2 \tan^2 x) - 9 \cos^2 x.$$\n\n2. **Recall the identity:** $$\tan^2 x = \frac{\sin^2 x}{\cos^2 x}.$$\n\n3. **Rewrite the expression using the identity:**\n$$B = 3 \cos^2 x \times \left(1 - 2 \frac{\sin^2 x}{\cos^2 x}\right) - 9 \cos^2 x.$$\n\n4. **Simplify inside the parentheses:**\n$$1 - 2 \frac{\sin^2 x}{\cos^2 x} = \frac{\cos^2 x - 2 \sin^2 x}{\cos^2 x}.$$\n\n5. **Substitute back:**\n$$B = 3 \cos^2 x \times \frac{\cos^2 x - 2 \sin^2 x}{\cos^2 x} - 9 \cos^2 x.$$\n\n6. **Cancel common factors:**\n$$B = 3 \cancel{\cos^2 x} \times \frac{\cos^2 x - 2 \sin^2 x}{\cancel{\cos^2 x}} - 9 \cos^2 x = 3 (\cos^2 x - 2 \sin^2 x) - 9 \cos^2 x.$$\n\n7. **Distribute 3:**\n$$B = 3 \cos^2 x - 6 \sin^2 x - 9 \cos^2 x.$$\n\n8. **Combine like terms:**\n$$B = (3 \cos^2 x - 9 \cos^2 x) - 6 \sin^2 x = -6 \cos^2 x - 6 \sin^2 x.$$\n\n9. **Factor out -6:**\n$$B = -6 (\cos^2 x + \sin^2 x).$$\n\n10. **Use Pythagorean identity:** $$\cos^2 x + \sin^2 x = 1,$$ so\n$$B = -6 \times 1 = -6.$$\n\n**Final answer:** $$B = -6.$$