The correct Active/Passive form of the given sentence is:

☀ The owner himself showed them the house.

Explanation for other options:

☀ The owner himself showing them the house. This option is not grammatically correct. The correct form should be "The owner himself showed them the house," not "The owner himself showing them the house." The sentence is in the present tense, but it should be in the past tense to match the original sentence.

☀ The owner himself was showed them the house. This option is not grammatically correct. The correct form should be "The owner himself showed them the house," not "The owner himself was showed them the house." The sentence is in the active voice, not the passive voice.

☀ The owner himself was showing them the house. This option is not grammatically correct. The correct form should be "The owner himself showed them the house," not "The owner himself was showing them the house." The sentence is in the past tense, not the continuous tense.