On the left, we have a 6 x 6 grayscale image, so we represent it using a 6 x 6 x 1 matrix because there are no separate RGB channels. To detect vertical edges, we construct a 3 x 3 matrix, called filter or kernel, shown in the middle. We convolve the 6 x 6 matrix with the 3 x 3 filter. The output of this convolution operator will be a 4 x 4 matrix.

To compute the upper left element of this 4 x 4 matrix, we take the 3 x 3 filter and paste it on top of the 3 x 3 region of the original input image and sum up all the 9 the element-wise products. So, the result would be 3 x 1 + 1 x 1 + 2 x 1 + 0 x 0 + 5 x 0 + 7 x 0 + 1 x (-1) + 8 x (-1) + 2 x (-1) = -5. Next, to compute the second element, we shift the pasted filter matrix one step to the right on the 6 x 6 image, do the same element-wise products, and then add them up, which will give us -4, and so on.

To compute the next rows, we shift the pasted filter matrix one step down on the 6 x 6 image. Then, we repeat the same element-wise products, and additions for the second row, and so on.