Determine if the graph is symmetric about the x-axis, the y-axis, or the origin. r = 4 - 3 sin θ origin only x-axis only y-axis only no symmetry

By graphing the given equation

r = 4 - 3 sin θ

We find that the graph is symmetric about the y-axis
The graph of the given equation is attached below
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Some information about the given equation:
the given equation is like the form of the Cardioid

A curve that is somewhat heart shaped. A cardioid can be drawn by tracing the path of a point on a circle as the circle rolls around a fixed circle of the same radius. The equation is usually written in polar coordinates.
Equations of Cardioid:  

r = a ± a cos θ (horizontal) or  r = a ± a sin θ (vertical)