Step 1: Recall that flame colour comes from the wavelength of light emitted, not just a memorised colour name.
When an alkali metal ion is heated in a flame, its outer electron jumps up and then falls back down, releasing a photon whose wavelength decides the colour we see.
Step 2: Match each metal to its dominant emission wavelength.
Cesium emits strongly in the blue region, around 455 to 460 nm. Potassium's emission is dominated by a line near 404 nm along with a red line, and the mixed effect is seen as a pale violet or lilac colour. Sodium has an extremely strong pair of lines at 589 nm, right in the yellow part of the spectrum. Lithium's strongest line sits near 671 nm, deep in the red end of the visible spectrum, giving its characteristic crimson colour.
Step 3: Line up wavelength with the colours listed in the figure.
Blue goes with cesium, violet goes with potassium, yellow goes with sodium, and crimson red goes with lithium.
Step 4: Read off the matching against the roman numerals.
Taking the metals in the order given in the question and pairing each with its wavelength-based colour reproduces the pairing cesium-blue, potassium-violet, sodium-yellow, lithium-crimson red.
Step 5: Compare with the options.
This pairing lines up exactly with option (3).
