Matchstick riddles usually challenge us to adjust a line here or there to alter a digital number. However, the puzzle gives an explicit warning at the bottom:
"HINT: Think OUTSIDE the box, not inside the digits!" The core prompt asks you to take the number 306 and make it bigger by moving only two sticks.
If you try to stay "inside the digits," the highest standard three-digit number you can make by shifting two sticks is 996 (by changing the 3 to a 9 and the 0 to a 9). While 996 is larger, it completely ignores the hint. To truly maximize the value, you have to think about exponents.
The absolute best way to solve this is by altering the final digit, the "6." Take the top horizontal matchstick and the bottom horizontal matchstick from the 6. This changes the 6 into a vertical line of two sticks, which looks like an 11.
Now, take those two removed sticks and place them at the top right of the remaining 30 to form a small exponent 11. Instead of a basic three-digit figure, you have created $30^{11}$ (30 to the power of 11). This yields a massive number in the trillions, perfectly fulfilling the challenge!