Find the value of $x$ .
Two right triangles are shown, triangle A B C and triangle D E F. Angle B and angle E are marked as right angles. Angle C and angle F are marked as being congruent. For triangle A B C, side A C is labeled x inches and side B C is labeled 6 inches. For triangle D E F, side D F is labeled 12 inches and side E F is labeled 8 inches.