let

l = the length of the original rectangle, l>o

w = the width of the original rectangle, w>0

a rectangle is twice as long as it is wide

l = 2w

if both its dimensions are increased by 4m, its area is increased by 88m^2

(l + 4)*(w + 4) - l*w = 88

plug l = 2w into the last equation

(2w + 4)*(w + 4) - 2w*w = 88

by solving we find

w = 6 m

click here to see the step by step solution of the equation

l = 2*6

l = 12 m

the original dimensions of the rectangle are: the length is 12 meters and the width is 6 meters.