Can someone explain how come the circled one is equal to zero but the other one is 6? I don't understand how they got that.

Answer:
The circled one has limit n tends to infinity on 3/n.
As 3 is a constant,it can come out of limit and the limit operates on 1/n.
Putting infinity in place of n,it becomes 1/(infinity),which is equal to 0.
Now,as for the other one,6 is a constant and limit on any constant gives the constant as it is.
So, it gives 6 .
Step-by-step explanation:
As n becomes very large, 3/n becomes very small. As n approaches infinity, 3/n approaches 0.
For limits of fractions:
If the power of the numerator (in this case, n⁰) is less than the power of the denominator (in this case, n¹), the limit as n approaches infinity is 0.
If the powers are equal, the limit as n approaches infinity is the ratio of the leading coefficients.
And if the power of the numerator is greater than the power of the denominator, the limit as n approaches infinity is infinity.
For the second limit, as n becomes very large, 6 is still 6. So as n approaches infinity, 6 approaches 6.