no worries!

x_n is a vector of 3 values. x_n = [x_n1, x_n2, x_n3]. Each value can be 0 or 1. So there could 8 (2 * 2 * 2) distinct set of x_n vector values.

In digital logic, the boolean values true/false are represented as 1 and 0. 1 is true and 0 is false.

in 6c) The problem defines g as XOR: "if the number of 1's in x is odd, g returns 1; if it is even g returns 0".

Consider x_n = [1,0,0] then, the number of 1 in this example is 1, which is odd, so g returns 1. so g(x_n) = 1.