Let, $P(M)$ be the probability that it rains on monday, $P(T)$ be the probability that it rains on the next day which is tuesday
Let, $P(T/M)$ be the probability that it rains on tuesday given that it rained the day before, which is monday, $P(M \cap T)$ be the probability that it rains on two consecutive days, monday and tuesday
$P(T/M)=0.6$
$P(T/\overline{M})=0.2$
$P(T/M)$ and $P(T/\overline{M})$ are mutually exclusive events
i.e. $P((T/M) \cup (T/\overline{M})) = P(T/M) + P(T/\overline{M}) = 0.8$
i.e. $P(T) = 0.8$
we have from conditional probability,
$P(M \cap T) = {P(M)}{P(T/M)} = P(M)(0.6)$ -------(1)
we also have,
$P(M \cup T) = P(M) + P(T) - P(M \cap T)$ -------(2)
using equations (1) & (2), we have,
$P(M \cup T) = P(M) + 0.8 - P(M)(0.6)$
$P(M) = \frac{5}{2}P(M \cup T) - 2$ -------(3)
we, know that the probability of any event is $\le 1$
set, $P(M \cup T) \le 1$ in equation (3) to get $P(M) \le \frac{1}{2}$
i.e. $0 \le P(M) \le \frac{1}{2}$