Back around 1920 my mother was taken on a road trip in the family Buick. It was a big family and the car had trouble getting up the hills in upstate NY. The older kids got out to reduce the weight and push if necessary.
Those days are over. No need to charge up the hill or for anyone to get out. Automatic transmissions are computer operated and know what is best for the engine. Just drive up. You can let it slow down to save gas. Use tow mode to prevent the engine from laboring.
While the rule to go down in the same gear you came up is good advice, it works best for stick shifts. With an automatic, I don't count which gear I'm in going up, and although the transmission automatically downshifts going downhill, I downshift lower. Saves brakes and is safer. I prefer a stick (if you can get one anymore; they are victims of cellphones—can't talk and shift at the same time), today's automatics are more efficient.