When a wire is stretched, its length increases while its area of cross-section remains unchanged. The resistance of a wire is directly proportional to its length and inversely proportional to its area of cross-section.

Let`s assume the original length of the wire to be L and the original resistance to be R. Since the wire is stretched to double its length, the new length becomes 2L.

According to Ohm`s law, the resistance (R`) is given by R` = R * (2L / L) = 2R.

Therefore, the resistance of the wire after stretching it to double its length becomes 2 times the original resistance.

Now let`s analyze each option:

Option 1: 2x ohm - This is incorrect. The resistance does double when the length is doubled.

Option 2: 0.5x ohm - This is incorrect. The resistance does not become half when the length is doubled.

Option 3: 4x ohm - This is the correct answer. The resistance becomes 4 times the original resistance when the length is doubled.

Option 4: 6x ohm - This is incorrect. The resistance does not become 6 times the original resistance when the length is doubled.

In conclusion