Let's define the next variables:
x: amount of singles
y: amount of doubles
z: amount of triples
Pamela had 46 hits, then:
x + y + z = 46 (eq. 1)
These hits totaled 67 bases, then:
x + 2y + 3z = 66 (eq. 2)
she had 4 times as many singles as doubles, then:
x = 4y (eq. 3)
Substituting equation 3 into equations 1 and 2, we get:
4y + y + z = 46
5y + z = 46 (eq. 4)
4y + 2y + 3z = 67
6y + 3z = 66 (eq. 5)
Isolating z from equation 4:
5y + z = 46
z = 46 - 5y (eq. 6)
Substituting equation 6 into equation 5, we get:
6y + 3(46 - 5y) = 66
6y + 3*46 - 3*5y = 66
6y + 138 - 15y = 66
6y - 15y = 66 - 138
-9y = -72
y = (-72)/(-9)
y = 8
She had 8 doubles.