Analysis
1. Identify the Contrast: The key to this sentence is the shift indicated by "has discarded" and "has concentrated on."
- Modern architecture has discarded (thrown away) the old style of trimming.
- Modern architecture concentrated on an "almost Greek simplicity of line." (Simple, plain, uncluttered).
2. Determine the Required Meaning: The word in the blank must describe the old style of trimming that is the opposite of "simplicity." We need words that mean highly decorative, elaborate, or showy.
3. Evaluate the Options:
- flamboyant: (Adj.) Tending to attract attention because of confidence, stylishness, and extravagance; highly elaborate or ornate. (Excellent Fit. Opposite of simple.)
- ornate: (Adj.) Made in an intricate shape or decorated with complex patterns; highly decorated. (Excellent Fit. Opposite of simple.)
- austere: (Adj.) Severe or strict in manner or appearance; having no comforts or luxuries; plain and simple. (Opposite of what is needed; this describes the new architecture.)
- inconspicuous: (Adj.) Not clearly visible or attracting attention; subtle. (Opposite of what is needed.)
- aesthetic: (Adj.) Concerned with beauty or the appreciation of beauty. (Too neutral.)
- derivative: (Adj.) Something based on another source; unoriginal. (Irrelevant to the style of decoration.)

The two words that mean highly decorative and fit the context opposing "simplicity" are flamboyant and ornate.