just have to start from the inputs at the left and follow the signals through the gates until the final output at the right.
repeat for each combination of inputs.

by formula, the equivalent formula is ...
F = (((NOT A) NOR B) OR C) NAND (C XOR (B AND (NOT D)))

A = 0, B = 0, C = 0, D = 0 gives
F = (((NOT 0) NOR 0) OR 0) NAND (0 XOR (0 AND (NOT 0)))
= ((1 NOR 0) OR 0) NAND (0 XOR (0 AND 1))
= (0 OR 0) NAND (0 XOR 0)
= 0 NAND 0
= 1

A = 0, B = 0, C = 0, D = 1 gives
F = (((NOT 0) NOR 0) OR 0) NAND (0 XOR (0 AND (NOT 1)))
= ((1 NOR 0) OR 0) NAND (0 XOR (0 AND 0))
= (0 OR 0) NAND (0 XOR 0)
= 0 NAND 0
= 1

A = 0, B = 0, C = 1, D = 0 gives
F = (((NOT 0) NOR 0) OR 1) NAND (1 XOR (0 AND (NOT 0)))
= ((1 NOR 0) OR 1) NAND (1 XOR (0 AND 1))
= (0 OR 1) NAND (1 XOR 0)
= 1 NAND 1
= 0

... and so on

summary
A B C D -> F
--------------
0 0 0 0 -> 1
0 0 0 1 -> 1
0 0 1 0 -> 0
0 0 1 1 -> 0
0 1 0 0 -> 1
0 1 0 1 -> 1
0 1 1 0 -> 1
0 1 1 1 -> 0
1 0 0 0 -> 1
1 0 0 1 -> 1
1 0 1 0 -> 0
1 0 1 1 -> 0
1 1 0 0 -> 1
1 1 0 1 -> 1
1 1 1 0 -> 1
1 1 1 1 -> 0