Explanation:
I am not sure if I understand you right about what is needed.
I would understand we need the angle BAC (at A).
first of all, this is a right-angled triangle.
Pythagoras applies :
c² = a² + b²
with c being the Hypotenuse (side opposite of the 90° angle).
in our case that means
AC² = x² + y² = 4² + 6² = 16 + 36 = 52
AC = sqrt(52)
now we can use the law of sine to get the other angles.
a/sin(A) = b/sin(B) = c/sin(C)
with the sides and the corresponding angles being opposite.
in our case
y/sin(A) = AC/sin(B) = AC/sin(90) = AC
sin(A) = y/AC = 6/sqrt(52) = 0.832050294...
the angle A = 56.30993247...° ≈ 56.3°