Rule Detection

As per the question,

And,

Similarly,

Hence, option (a) is the correct answer.

According to the question,

As,

1 number is common in first two position of dices.

Now, start with 1 number, writing all the remaining numbers in clockwise direction.

Hence, 3 number will be on the face opposite to the one showing 6.

The number of triangles in the figure are :

$\Delta$ABE, $\Delta$AEC, $\Delta$CED, $\Delta$BED, $\Delta$ADC, $\Delta$CDB, $\Delta$ABC, $\Delta$ABD, $\Delta$PON, $\Delta$QOR, $\Delta$POQ, $\Delta$NQR, $\Delta$PNQ, $\Delta$PQR, $\Delta$NQR, $\Delta$NPR, $\Delta$CFG, $\Delta$CDG, $\Delta$CHF, $\Delta$HFG, $\Delta$KPN, $\Delta$KLN, $\Delta$KLM, $\Delta$LMN, $\Delta$BGI, $\Delta$BIJ, $\Delta$JIK, $\Delta$BIK, $\Delta$KIQ, $\Delta$KNQ and $\Delta$BCG = 31

From the given four positions of a single block, Faces adjacent to face having red colour = blue, pink, yellow, green

Clearly, black is opposite to red.