We present a multiwavelength analysis of a long-duration, white-light solar flare (M8.9/3B) event that occurred on 04 June 2007 from AR NOAA 10960. The flare was observed by several spaceborne instruments, namely SOHO/MDI, Hinode/SOT, TRACE, and STEREO/SECCHI. The flare was initiated near a small, positive-polarity, satellite sunspot at the center of the active region, surrounded by opposite-polarity field regions. MDI images of the active region show a considerable amount of changes in the small positive-polarity sunspot of δ configuration during the flare event. SOT/G-band (4305 Å) images of the sunspot also suggest the rapid evolution of this positive-polarity sunspot with highly twisted penumbral filaments before the flare event, which were oriented in a counterclockwise direction. It shows the change in orientation, and also the remarkable disappearance of twisted penumbral filaments (≈35 – 40%) and enhancement in umbral area (≈45 – 50%) during the decay phase of the flare. TRACE and SECCHI observations reveal the successive activation of two helically-twisted structures associated with this sunspot, and the corresponding brightening in the chromosphere as observed by the time-sequence of SOT/Ca ii H line (3968 Å) images. The secondary, helically-twisted structure is found to be associated with the M8.9 flare event. The brightening starts six – seven minutes prior to the flare maximum with the appearance of a secondary, helically-twisted structure. The flare intensity maximizes as the secondary, helically-twisted structure moves away from the active region. This twisted flux tube, associated with the flare triggering, did not launch a CME. The location of the flare activity is found to coincide with the activation site of the helically-twisted structures. We conclude that the activation of successive helical twists (especially the second one) in the magnetic-flux tubes/ropes plays a crucial role in the energy build-up process and the triggering of the M-class solar flare without a coronal mass ejection (CME).