In the following reaction, 'B' is

1. Protonation of the Alcohol

The lone pair of electrons on the oxygen atom of the secondary alcohol $$(-\text{OH}$$) attacks a hydronium ion $$(\text{H}^{+}$$).

The hydroxyl group is converted into an excellent leaving group, a protonated water molecule $$(-\text{OH}_{2}^{+}$$).

2. Loss of Water (Carbocation Formation)

The $$\text{C}-\text{O}$$ bond breaks, and water $$(\text{H}_2\text{O}$$) leaves.

A secondary $$(2^{\circ }$$) carbocation is formed on the carbon chain adjacent to the bulky tert-butyl group.

3. 1,2-Methyl $$(\text{CH}_{3}^{-}$$) Shift

A secondary carbocation is relatively unstable. To gain stability, a methyl group from the adjacent tert-butyl group migrates with its electron pair (a 1,2-methyl shift) to the carbocation carbon.

This rearranges the less stable $$2^{\circ }$$ carbocation into a highly stable tertiary $$(3^{\circ })$$ carbocation at the terminal branch.

4. Intramolecular Cyclization (Ring Closure) 

The $$\pi$$-electrons of the cyclohexene double bond act as an intramolecular nucleophile, attacking the newly formed tertiary carbocation.

This nucleophilic attack closes the chain into a second 6-membered ring (forming a fused decalin system). A new tertiary carbocation is generated at the ring junction (bridgehead position).

5. Deprotonation $$(-\text{H}^{+})$$ to Form the Major Product

A weak base (such as water) removes a proton $$(\text{H}^{+})$$ from the adjacent carbon atom at the ring junction.

Elimination of the proton forms a highly stable, tetrasubstituted double bond directly at the shared bridgehead position between the two fused 6-membered rings.