Installing Washer In Room Below Ground Level

A washing machine pump is designed to pump water about 2 - 3 feet. If the drain hose is fixed an extra 3 feet above the top of the washing machine it would increase the height to 6 feet and although the water would possibly pump out the flow will be substantially reduced. It's unlikely a washing machine could pump water fast enough to either rinse properly, or to not time out (and abort) on empty.

If your washing machine would only have to pump 3 feet in total, and then run 12 feet it could work although it couldn't pump the water 3 feet plus a further 12 feet so the last section would have to have a decent slope towards the drain.

You can buy a proper pump system that can pump water quite a long way, designed for washing machines in a basement needing to pump upstairs Saniflow make such pumps. Some of their pumps can allow a washing machine to pump up to 5 metres high.

Finally, raising the washing machine itself by installing it on a secure platform and hemmed in so it can't fall off can reduce the height needed to work properly.