Identify the figure in the options that when put in place of the question mark (?) will logically complete the series?

To logically complete the series, let us analyze the pattern of the numbers positioned around the shape 'N' in each successive figure of the sequence.

Each figure contains three numbers located at three distinct positions: bottom-left (below the diagonal), top-right (above the diagonal), and to the right of the vertical line.

1. Bottom-Left Number (below the diagonal):

The sequence of numbers at the bottom-left is:

$2,4,6,8,\dots$

This is an arithmetic sequence increasing by $2$ at each step.

Therefore, the next bottom-left number is:

$8+2=10$

2. Top-Right Number (above the diagonal):

The sequence of numbers at the top-right position is:

$4,6,8,10,\dots$

This is also an arithmetic sequence increasing by $2$ at each step.

Therefore, the next top-right number is:

$10+2=12$

3. Right-Side Number (outside the vertical line):

The sequence of numbers on the right side is:

$6,10,14,18,\dots$

This is an arithmetic sequence increasing by $4$ at each step (which also equals the sum of the bottom-left and top-right numbers: $2+4=6$, $4+6=10$, $6+8=14$, $8+10=18$).

Therefore, the next right-side number is:

$18+4=22$ (or $10+12=22$)

Thus, the required figure must have 10 at the bottom-left, 12 at the top-right, and 22 on the right side.

This corresponds to the first option figure: