The correct answer is: Amalgamation.

Amalgamation is a type of merger in which two or more companies combine to form a new company. The old companies cease to exist and the new company takes their place.

Internal reconstruction is a type of restructuring in which a company changes its capital structure without changing its legal identity. This can be done by issuing new shares, buying back shares, or converting debt into equity.

Absorption is a type of merger in which one company acquires another company. The acquired company ceases to exist and becomes a subsidiary of the acquiring company.

External reconstruction is a type of restructuring in which a company sells off some of its assets or businesses. This can be done to raise cash, to focus on core businesses, or to comply with regulations.

In conclusion, amalgamation is the only option in which both of the old companies will not exist.