Let's translate the English into math . . .
Let X = the number of 6 hour shifts
"She worked 4 times as many 8 hour shifts as 6 hour shifts" so the number of 8 hour shifts = 4X
The number of hours worked during those 6 hour shifts = 6X.
The number of hours worked during those 8 hour shifts = 8(4X) = 32X
"Jane worked 38 hours" so 38 =6X + 32X
Combine like terms on the right side
38 = 38X
Divide both sides by 38
X = 1
That means there was one 6-hour shift and four 8-hour shifts