When Jerome picks two cards from a set of cards numbered 1-4, there are several possible sums that the two cards could equal. Let's consider each possible combination:
1. If Jerome picks two cards with the numbers 1 and 1, the sum of the two cards would be 2.
2. If Jerome picks two cards with the numbers 1 and 2, the sum of the two cards would be 3.
3. If Jerome picks two cards with the numbers 1 and 3, the sum of the two cards would be 4.
4. If Jerome picks two cards with the numbers 1 and 4, the sum of the two cards would be 5.
5. If Jerome picks two cards with the numbers 2 and 2, the sum of the two cards would be 4.
6. If Jerome picks two cards with the numbers 2 and 3, the sum of the two cards would be 5.
7. If Jerome picks two cards with the numbers 2 and 4, the sum of the two cards would be 6.
8. If Jerome picks two cards with the numbers 3 and 3, the sum of the two cards would be 6.
9. If Jerome picks two cards with the numbers 3 and 4, the sum of the two cards would be 7.
10. If Jerome picks two cards with the numbers 4 and 4, the sum of the two cards would be 8.
Thus, the possible sums that the two cards could equal are 2, 3, 4, 5, 6, 7, and 8.