Let's start by decoding the function. Since I've not seen an SOP (sum of products) problem written this way, I'm going to assume that each constant in the Σ(2,4,7,10,12) part corresponds to the decimal equivalent of the (w,x,y,z) values where true == 1, and w == 2^3, x == 2^2, y == 2^1, and x == 2^0. With these assumptions, then, the truth table for the function is:
w x y z | f()
0 0 0 0 | 0. 0
0 0 0 1 | 0. 1
0 0 1 0 | 1. 2 <-
0 0 1 1 | 0. 3
0 1 0 0 | 1. 4 <-
0 1 0 1 | 0. 5
0 1 1 0 | 0. 6
0 1 1 1 | 1. 7 <-
1 0 0 0 | 0. 8
1 0 0 1 | 0. 9
1 0 1 0 | 1. 10 <-
1 0 1 1 | 0. 11
1 1 0 0 | 1. 12 <-
1 1 0 1 | 0. 13
1 1 1 0 | 0. 14
1 1 1 1 | 0. 15
By inspection, we can already see that the only difference between the values 2 and 10, and between the values 4 and 12, is the value of w; we can then ignore w, reducing (2,10) and (4,12) to 2 (X'YZ') and 4 (XY'Z'), respectively. The 7 value (W'XYZ) remains, unchanged. So, the final SOP is:
X'YZ'+XY'Z'+W'XYZ
(or, in the original form: Σ(2,4,7))
