The correct answer is the star symbol ($✶$).

To find the symbol that occupies the box marked with a question mark (?), we can solve the grid step-by-step by applying the two given rules:
1. Every row and every column must contain each of the four symbols: Circle ($◯$), Star ($✶$), Triangle ($△$), and Square ($☐$).
2. Every $2\times 2$ square delineated by bold lines must contain each of the four symbols.

Let us denote the cells in the grid using the row number ($R$ from 1 to 4, top to bottom) and column number ($C$ from 1 to 4, left to right). The initial state of the grid shown in the image is as follows:
• Row 1: Cell (1, 1) is empty, Cell (1, 2) is ?, Cell (1, 3) is empty, and Cell (1, 4) is Triangle ($△$).
• Row 2: Cell (2, 1) is empty, Cell (2, 2) is Circle ($◯$), Cell (2, 3) is Star ($✶$), and Cell (2, 4) is empty.
• Row 3: Cell (3, 1) is empty, Cell (3, 2) is empty, Cell (3, 3) is Square ($☐$), and Cell (3, 4) is Star ($✶$).
• Row 4: Cell (4, 1) is Star ($✶$), Cell (4, 2) is empty, Cell (4, 3) is Triangle ($△$), and Cell (4, 4) is Circle ($◯$).

Step 1: Fill in Column 3
Looking at Column 3, we have the following entries:
• Cell (2, 3) contains Star ($✶$)
• Cell (3, 3) contains Square ($☐$)
• Cell (4, 3) contains Triangle ($△$)
Since every column must contain all four symbols, the remaining cell in this column, which is Cell (1, 3), must contain the only missing symbol, which is the Circle ($◯$).
Thus, Cell (1, 3) = $◯$.

Step 2: Determine missing symbols in Row 1
Now we examine Row 1. The entries are:
• Cell (1, 2) is the target box ?
• Cell (1, 3) contains Circle ($◯$)
• Cell (1, 4) contains Triangle ($△$)
The two missing symbols for Row 1 are the Star ($✶$) and the Square ($☐$). Therefore, the box marked with ? (Cell (1, 2)) must be either $✶$ or $☐$.

Step 3: Determine missing symbols in Column 2
Let us examine the entries in Column 2:
• Cell (2, 2) contains Circle ($◯$)
• Cell (4, 2) must contain Square ($☐$) because Row 4 already has Star ($✶$), Triangle ($△$), and Circle ($◯$).
With Cell (2, 2) containing Circle ($◯$) and Cell (4, 2) containing Square ($☐$), the remaining cells in Column 2 (which are Cell (1, 2) and Cell (3, 2)) must contain the two remaining symbols: Star ($✶$) and Triangle ($△$).

Step 4: Resolve the value of '?'
Comparing the requirements from Step 2 and Step 3:
• From Row 1: The box ? (Cell (1, 2)) must be either Star ($✶$) or Square ($☐$).
• From Column 2: The box ? (Cell (1, 2)) must be either Star ($✶$) or Triangle ($△$).
Taking the intersection of these two sets of possibilities, the only symbol that satisfies both conditions is the Star ($✶$).
Therefore, the box marked with ? must occupy the Star ($✶$) symbol.