Note that

Z = (Y-µ)/σ

is a standard normal random variable.

When we apply it to the given probabilities, they become

P(Z > (47-µ)/σ) = 0.1587

P(Z < (46-µ)/σ) = 0.6915

Now looking at a z-table, we may conclude that

(47-µ)/σ = 1

(46-µ)/σ = 0.5

Considering this as a system of equations in the variables µ and σ, we just solve algebraically to get

µ = 45

σ = 2

and of course, by squaring the standard deviation, we find a variance of

σ^2 = 4.