I am a US citizen and I want to transfer some amount 10 lakhs+ to my brother from my NRE account in India to his account. My brother is going to purchase something for his business. He is going to return my amount after 3-4 Months

From the description it looks like you would like to loan to your brother on repatriation basis. Yes this is allowed. See the RBI Guide here and here for more details. There are some conditions;

(iv) Scheme for raising loans from NRIs on repatriation basis
Borrowings not exceeding US$ 2,50,000 or its equivalent in foreign exchange by an individual resident in India from his close relatives resident outside India, subject to the conditions that -

a) the loan is free of interest; b) the minimum maturity period of the loan is seven years; c) The amount of loan is received by inward remittance in free foreign exchange through normal banking channels or by debit to the NRE/FCNR account of the non-resident lender; d) The loan is utilised for the borrower's personal purposes or for carrying on his normal business activity but not for carrying on agricultural/plantation activities, purchase of immovable property or shares/debentures/bonds issued by companies in India or for re-lending.

Although it is mentioned as Seven years, this is revised to one year.

Since he cannot deposit into my NRE account I guess he has to deposit it into my NRO account.

A repatriate-able loan as above can be deposited into NRE Account.

Is there any illegality here doing such transaction? No. Please ensure proper paper work to show this as loan and document the money trail.

Also once I get my money in NRO account do I need to pay taxes in India on the money he deposited?

This question does not arise.

I am a US citizen and I want to transfer some amount 10 lakhs+ to my brother from my NRE account in India to his account. My brother is going to purchase something for his business. He is going to return my amount after 3-4 Months

From the description it looks like you would like to loan to your brother on repatriation basis. Yes this is allowed. See the RBI Guide here and here for more details. There are some conditions;

(iv) Scheme for raising loans from NRIs on repatriation basis
Borrowings not exceeding US$ 2,50,000 or its equivalent in foreign exchange by an individual resident in India from his close relatives resident outside India, subject to the conditions that -

a) the loan is free of interest; b) the minimum maturity period of the loan is seven years; c) The amount of loan is received by inward remittance in free foreign exchange through normal banking channels or by debit to the NRE/FCNR account of the non-resident lender; d) The loan is utilised for the borrower's personal purposes or for carrying on his normal business activity but not for carrying on agricultural/plantation activities, purchase of immovable property or shares/debentures/bonds issued by companies in India or for re-lending.

Although it is mentioned as Seven years, this is revised to one year.

Since he cannot deposit into my NRE account I guess he has to deposit it into my NRO account.

A repatriate-able loan as above can be deposited into NRE Account.

Is there any illegality here doing such transaction?

No. Please ensure proper paper work to show this as loan and document the money trail.

Also once I get my money in NRO account do I need to pay taxes in India on the money he deposited?

This question does not arise.