[Grade 12 Calculus: Double Integrals] How do I decide whether to use dx or dy as the inner integral

I am working on a double integral problem over a triangular region. I drew the region and I understand the concept of integrating over strips. But I keep getting stuck on whether to integrate with respect to x first or y first. My instructor said to look at the shape of the strip. If the strip is vertical then inner integral is dy and outer is dx. If the strip is horizontal then inner integral is dx. But sometimes both seem to work. How do I know which order makes the integral easier to set up in terms of bounds. Is there a rule of thumb.