Calculate the areas of the shapes ABJH, BCDJ, DEFJ, and HJFG.

ABJH is a square with side length $AB = AH = x$ units.

Area of ABJH $= \text{side} \times \text{side} = x \times x = x^2$ units$^2$.
The area of ABJH is $\boxed{x^2 \text{ Units}^2}$.

1.1.2 BCDJ

BCDJ is a rectangle. Its length is $BC = 6$ units. Its width is $BJ$. Since ABJH is a square, $BJ = AH = x$ units.

Area of BCDJ $= \text{length} \times \text{width} = BC \times BJ = 6 \times x = 6x$ units$^2$.
The area of BCDJ is $\boxed{6x \text{ Units}^2}$.

1.1.3 DEFJ

DEFJ is a rectangle. Its length is $JD$. From the diagram, $JD = BC = 6$ units. Its width is $JF$. From the diagram, $JF = HG = 4$ units.

Area of DEFJ $= \text{length} \times \text{width} = JD \times JF = 6 \times 4 = 24$ units$^2$.
The area of DEFJ is $\boxed{24 \text{ Units}^2}$.

1.1.4 HJFG

HJFG is a rectangle. Its length is $HG = 4$ units. Its width is $HJ$. Since ABJH is a square, $HJ = AB = x$ units.

Area of HJFG $= \text{length} \times \text{width} = HG \times HJ = 4 \times x = 4x$ units$^2$.
The area of HJFG is $\boxed{4x \text{ Units}^2}$.

1.2.1 AC

The length $AC$ is the sum of the lengths of segments $AB$ and $BC$.

$AC = AB + BC = x + 6$ units.
The length of AC is $\boxed{x+6 \text{ Units}}$.

1.2.2 AG

The length $AG$ is the sum of the lengths of segments $AH$ and $HG$.

$AG = AH + HG = x + 4$ units.
The length of AG is $\boxed{x+4 \text{ Units}}$.