Step 1: What the question asks.
Two tables have degrees 3 and 4. We need the degree of their Cartesian product.
Step 2: Build a tiny model.
Let table P have columns (a, b, c) and table Q have columns (d, e, f, g). A row of the product is one row of P joined to one row of Q.
Step 3: Count the columns of a product row.
Such a row has the values for a, b, c, d, e, f, g. That is 7 columns, so the degree is 7.
Step 4: Do not confuse with rows.
If P had 5 rows and Q had 6 rows, the product would have $5 \times 6 = 30$ rows. The multiplication belongs to rows only. The columns just add.
Step 5: Why 12 is a trap.
12 comes from multiplying 3 and 4. That mixes the rule for rows with the rule for columns.
Step 6: Match with the options.
The number 7 is the third printed option.
Step 7: Why each wrong option fails.
The value 3 and the value 4 are the degrees of the single tables, so each leaves out the columns of the other table. The value 12 is the product of the two degrees and does not count any columns. Only the sum 7 counts every column once, so options 1, 2 and 4 are wrong.
Final Answer:
Degree = 3 + 4 = 7, so the answer is option 3.
\[ \boxed{7} \]