To find the final price of an item after two successive price increases, we can follow these steps:

1. First Increase:
- The original price is \( x \).
- The price is increased by 20%.
- New price after the first increase:
\[
\text{New Price} = x + 0.20x = 1.20x
\]

2. Second Increase:
- This new price is then increased by 30%.
- New price after the second increase:
\[
\text{New Price} = 1.20x + 0.30 \times 1.20x = 1.20x \times (1 + 0.30) = 1.20x \times 1.30
\]
- Calculate:
\[
1.20 \times 1.30 = 1.56
\]

Thus, the final price after the two increments is \( 1.56x \).

The correct answer is B. 1.56x.