I am an Indian passport holder and applied for a 6-month UK visitor visa to visit my daughter, who is a British citizen. My question is very specific. If I am granted a multipe-entry visa for 6 months, starting on May 1, 2017, and I stay in the UK for 2 months, from June 1 to July 31, 2017, can I visit again for two months from October 1 to November 30, 2017 or do I have to come back before the expiry of the 6 months ie October 30, 2017, even though my total stay in the UK is not exceeding 4 months?
If your visa is valid for six months, then you can stay only until the expiry date. You must leave on or before this date.
If your visa is valid for longer than six months, then you may be granted up to six months' stay each time you enter the UK, but never beyond the visa's expiry date. In addition, if the immigration officer thinks that you are trying to abuse the system, you may be given a shorter period of admission.
Because your visa must be valid for the entire duration of your stay in the UK, if your visa is valid until 30 October, you will need to leave on or before that date.
More information about the Standard Visitor Visa may be found at https://www.gov.uk/standard-visitor-visa/overview.
You can apply to extend your visa while you are in the UK, but as you can see from the linked page, it is quite expensive, costing £993 to apply by post and £1583 to apply in person. If you want to stay from 1 October to 30 November then you will probably be better off applying for a second visa in August while you are outside the UK.