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.