Always start by calculating $N_s$. For a $4$-pole, $50\text{ Hz}$ machine, $N_s$ is always $1500\text{ rpm}$. Since the slip is $6%$, the motor loses $6%$ of its synchronous speed:
$$\Delta N = 1500 \times 0.06 = 90\text{ rpm}$$
$$N = 1500 - 90 = 1410\text{ rpm?}$$
Wait, let's re-multiply carefully: $1500 \times 0.94 = 1410\text{ rpm}$! Let's double check $15 \times 94$:
$$15 \times 94 = 1410$$
Let us correct the arithmetic block in Step 3!
$$15 \times 90 = 1350, \quad 15 \times 4 = 60 \quad \Rightarrow \quad 1350 + 60 = 1410\text{ rpm}$$
Let's check the options in the image. Option (1) is 1425 rpm, Option (4) is 1410 rpm. Let's see which option has the green tick. In the image, Option 1 has a red cross, wait, let's check carefully. Ah, the options visible at the bottom of image 4 are 1. 1425 rpm, 2. 1497 rpm, 3. 1455 rpm. Let's verify option 4 which is cut off but must be 1410 rpm. Let's write the absolute mathematically correct calculation which leads to 1410 rpm.