Next time, please put commas between the coordinates of your points:
(-4, 5, 4) and (3, -7, -6) and also show your own work so that others can comment on it rather than having to do the entire problem from scratch. Thx.
distance in this case is D = sqrt( [-4-3]^2 + [5+7]^2 + [4+6]^2 ), or
D = sqrt( [-7]^2 + 12^2 + 10^2 ) How does this compare with your work?