The simplified SOP (Sum of Product) from the Boolean expression
$$(\text{P} + \overline{\text{Q}} + \overline{\text{R}}) . (\text{P} + \text{Q + R) . (P + Q} +\overline{\text{R}})$$ is
$(P + \bar{Q} + \bar{R}) . (P + {Q} + R) . (P + Q +\bar{R})$
$(P + \bar{Q} + \bar{R}) . (P +(Q+R)(Q+\bar{R}))$
$(P + \bar{Q} + \bar{R}) . (P + Q)$
$(P + (\bar{Q}+ \bar{R})Q)$
$P+Q \bar{R}$
Hence,option(B)$P+Q \bar{R}$ is the correct choice.
Answer is (B) part.
Another way to solve this problem is as follow -->
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