Question 375994
With those constraint we can imagine there are an infinite number of ways, except if the sub areas are rectangles too, which was not specified.

If the area have to have the same shape, there are 2 possibilities

the length divided by 3, 3 rectangle 1 times 2
{{{drawing(300,300,0,4,0,4,grid(1),
green(line(0,0,3,0),
line(3,0,3,2),
line(3,2,0,2),

line(1,0,1,2),
line(2,0,2,2)))}}}
 
 
the height divided by 3 : 3 rectangles 2/3 times 3
{{{drawing(300,300,0,4,0,4,grid(1),
green(line(0,0,3,0),
line(3,0,3,2),
line(3,2,0,2),

line(0,2/3,3,2/3),
line(0,4/3,3,4/3)))}}}
 
 
if they can be rectangles not forcedly the same, 2 more possibilities :
1 vertical, 2x3/4, and 2 horizontal 1x9/4
{{{drawing(300,300,0,4,0,4,grid(1),
green(line(0,0,3,0),
line(3,0,3,2),
line(3,2,0,2),

line(4/3,0,4/3,2),
line(4/3,1,3,1)))}}}
 
 
1 horizontal : 3x2/3, and 2 vertical : 3/2x4/3
 {{{drawing(300,300,0,4,0,4,grid(1),
green(line(0,0,3,0),
line(3,0,3,2),
line(3,2,0,2),

line(0,2/3,3,2/3),
line(3/2,2,3/2,2/3)))}}}


if other shapes are allowed the number is infinite, like : 
1 rectangle 2x4/3 and 2 triangles
 {{{drawing(300,300,0,4,0,4,grid(1),
green(line(0,0,3,0),
line(3,0,3,2),
line(3,2,0,2),

line(4/3,0,4/3,2),
line(4/3,0,3,2)))}}}