Here u wrote p(x= 0) = 1/16 but it should be 0/16

The probability $P(X=0)$ represents the probability of getting zero heads when tossing four fair coins.
There is only one way to get zero heads: TTTT (Tail, Tail, Tail, Tail).
Since there are $2^4 = 16$ total possible outcomes when tossing four coins, the probability of getting zero heads is $\frac{1}{16}$.

So, $P(X=0) = \frac{1}{16}$ is correct.

The term $0 \left(\frac{1}{16}\right)$ in the expectation calculation $E[X] = \sum x P(X=x)$ is the contribution of $x=0$ to the sum. This term simplifies to 0, but it uses the correct probability $P(X=0) = \frac{1}{16}$.

If $P(X=0)$ were $0/16$, it would mean it's impossible to get zero heads, which is not true for four coin tosses.

What else can I help with?