Solved grid:

The key idea here is different from the usual Nurikabe. Usually, we start with finding numbers separated by one square (shaded square in between), or from squares numbered 1 (shades all around).

But here,

we first calculate the total area of unshaded squares, which is 9+8+12+20 = 49. The grid is 8x8, so total shaded area is 64-49 = 15.

Now, consider the following green region:

At least one of the green squares are shaded, otherwise, 9 will connect to 8. Similarly, there is at least one shaded square on the right edge (red), bottom edge (yellow), and left edge (blue).

Based on the rules of Nurikabe, all shaded squares are connected, and we also observe:

to connect the shaded square(s) in top edge to the bottom edge, at least one square of each row (excluding the edges) needs to be shaded. This requires at least 6 shaded squares (excluding the edges). Similarly, to connect the shaded square(s) in left edge to the right edge, at least one square of each column (excluding the edges) needs to be shaded. This requires at least 5 more shaded squares, since we already have at least one column covered by the first step.
Including the at least 4 squares at the edges, we already covered the only 15 shaded squares that we have.
This means we need to connect the edge squares in more or less straight lines, with no leftover budget to spare. This will divide the 8x8 grid into 4 rectangular unshaded regions.
This means the unshaded region containing the 9 must be 3x3 (1x9 is impossible), and the unshaded region containing the 20 must be 4x5 (2x10 and 1x20 is impossible), and the unshaded region containing the 9 must be 2x4 (1x8 is impossible since it'll hit 9 or 20). These unshaded regions should cover the corners, so the region containing 9 is fixed, and since there can be no 2x2 shaded squares, the orientation of the unshaded region containing 8 is also fixed (can only be yellow+red in the image below:)

And with 4 shaded squares left, there is only one possible way to make the rectangular region containing the 12, as per the solution.

Solved grid:

The key idea here is different from the usual Nurikabe. Usually, we start with finding numbers separated by one square (shaded square in between), or from squares numbered 1 (shades all around).

But here,

we first calculate the total area of unshaded squares, which is 9+8+12+20 = 49. The grid is 8x8, so total shaded area is 64-49 = 15.

Now, consider the following green region:

At least one of the green squares are shaded, otherwise, 9 will connect to 8. Similarly, there is at least one shaded square on the right edge (red), bottom edge (yellow), and left edge (blue).

Based on the rules of Nurikabe, all shaded squares are connected, and we also observe:

to connect the shaded square(s) in top edge to the bottom edge, at least one square of each row (excluding the edges) needs to be shaded. This requires at least 6 shaded squares (excluding the edges). Similarly, to connect the shaded square(s) in left edge to the right edge, at least one square of each column (excluding the edges) needs to be shaded. This requires at least 5 more shaded squares, since we already have at least one column covered by the first step.
Including the at least 4 squares at the edges, we already covered the only 15 shaded squares that we have.
This means we need to connect the edge squares in more or less straight lines, with no leftover budget to spare. This will divide the 8x8 grid into 4 rectangular unshaded regions.
This means the unshaded region containing the 9 must be 3x3 (1x9 is impossible), and the unshaded region containing the 20 must be 4x5 (2x10 and 1x20 is impossible), and the unshaded region containing the 9 must be 2x4 (1x8 is impossible since it'll hit 9 or 20). These unshaded regions should cover the corners, so the region containing 9 is fixed, and since there can be no 2x2 shaded squares, the orientation of the unshaded region containing 8 is also fixed (can only be yellow+red in the image below:)

And with 4 shaded squares left, there is only one possible way to make the rectangular region containing the 12, as per the solution.

As for the title, "Back to Basic",

I think it's about the simple multiplications for the areas, as in they are basic maths? Or it can also refer to the fact that we rely quite strongly on one of the basic rules of Nurikabe, the connectivity of shaded squares?