At what height above earth's surface is the gravitational acceleration reduced from its sea-level value by 0.40%?

At sea level, you're 6400 km away from the earth's center. Where gravity is 0.4 fewer,

in other words 0.6 its sea level value, you're x km from the center, where:

(6400 / x) ^ 2 = 0.6)

Take note that gravity is an opposite square force.

So 6400 / x = 0.7746

so x = 8262 km from the Earth's center

so you're 8262 – 6400 = 1862 km above the Earth's surface