The question asks us to identify the Himalayan river that does not originate from across the Himalayas. Let`s analyze each option to determine the correct answer.

Option 1: Indus - The Indus river originates in the Tibetan plateau, which is situated across the Himalayas. Therefore, this option does not fit the criteria.

Option 2: Satluj - The Satluj river also originates in the Tibetan plateau, across the Himalayas. Therefore, this option does not meet the requirement.

Option 3: Ganga - The Ganga river is the correct answer. It is the only Himalayan river that does not originate from across the Himalayas. The Ganga river`s source is the Gangotri glacier in the Indian state of Uttarakhand, which is located within the Indian subcontinent.

Option 4: Brahmaputra - The Brahmaputra river originates in the Tibetan plateau, just like the other two options. It flows across the Himalayas and enters Assam, India. Therefore, this option does not satisfy the condition stated in the question.

To summarize, the correct answer is option 3 - Ganga, as it is the only Himalayan river that does not originate from across the Himalayas.