We study the X-ray and optical properties of the ultraluminous X-ray source (ULX) X-6 in the nearby galaxy NGC 4258 (M106) based on the archival XMM-Newton, Chandra, Swift, and Hubble Space Telescope (HST) observations. The source has a peak luminosity of L-X similar to 2 x 10(39) erg s(-1) in the XMM-Newton observation of 2004 June. Consideration of the hardness ratios and the spectral model parameters shows that the source seems to exhibit possible spectral variations throughout the X-ray observations. In the images from the HST/Advanced Camera for Surveys, three optical sources have been identified as counterpart candidates within the 1 sigma error radius of 0 ''.3. The brightest one has an absolute magnitude of M-V approximate to -7.0 and shows extended structure. The remaining two sources have absolute magnitudes of M-V approximate to -5.8 and -5.3. The possible spectral types of the candidates from brightest to dimmest were determined as B6-A5, B0-A7, and B2-A3. The counterparts of the X-ray source possibly belong to a young star cluster. Neither the standard disk model nor the slim disk model provides firm evidence to determine the spectral characteristics of ULX X-6. We argue that the mass of the compact object lies in the range 10-15M(circle dot), indicating that the compact source is most likely a stellar-mass black hole.