The area enclosed by the curve |x + 1| + |y + 1| = 2 is

Shift the origin at the point (-1, -1)

So |x + 1| + |y + 1| = 2 becomes |x| + |y| = 2

Hence required area is

= $4 \times \frac{1}{2} \times 2 \times 2$ = 8 sq. units