The quadriceps muscle group is primarily responsible for the extension of the knee. This group includes the rectus femoris, vastus lateralis, vastus medialis, and vastus intermedius. The biceps femoris part of the hamstring muscle group and is responsible for the flexion of the knee.

The flexor digitorum brevis is sandwiched between the plantar aponeurosis and the tendons of the flexor digitorum longus. It flexes the lateral four digits at the proximal interphalangeal joints.

The gluteus maximus is innervated by the inferior gluteal nerve. The gluteus medius and minimus are innervated by the superior gluteal nerve. The femoral nerve does not innervate the glutes, and the obturator nerve innervates muscles in the medial thigh. 

The short head of the biceps femoris is the only muscle of the posterior thigh that is not part of the "hamstring" muscle group. It is not cosnidered a hamstring muscle because it only crosses the knee joint; it does not act on the hip joint. 

Only the short head of the biceps femoris is innervatd by the common fibular division of the sciatic nerve. The long head of the biceps femoris, the semimembranous, and the semitendinous are innervated by the tibial division of the sciatic nerve. The gluteus maximus is innervated by the inferior gluteal nerve.

All of the incorrect answer options are muscles of the anterior compartment of the leg. Muscles of the anterior compartment are involved in dorsiflexion of the ankle and are all innervated by the deep fibular nerve.

The fibularis longus is a muscle of the lateral comaprtment of the leg. Muscles of the lateral compartment of the leg are innervated by the superficial fibular nerve.

The piriformis passes through the greater sciatic notch and, in some people, is pierced by the sciatic nerve. 

We are looking for a muscle in the anterior/medial compartment of the thigh. Based on this we can eliminate the tensor fasia latae and vastus lateralis muscles because they are not in this compartment. The vastus lateralis muscle is part of the quadriceps, meaning it inserts into the tibial tuberosity via the quadriceps tendon, and is the lateralmost of the four quadriceps muscles. The adductor brevis does originate on the pubis, but it inserts on the femur, not the tibia, and its action is adduction of the femur. That leaves us with only the gracilis muscle as the right answer. The action of the gracilis is primarily flexion of the tibia, but it also medially rotates and adducts the hip.

The semitendinosus, gracilis, and sartorius are the three muscles that make up the pes anserine group, coming from the posterior, medial, and anterior compartments of the thigh, respectively. The adductor longus, is not part of this group as it inserts on the linea aspera of the femur, rather than the pes anserinus, like the semitendinosus, gracilis, and sartorius.

No muscles attach to the talus directly. However, the extensor digitorum brevis comes close, via its attachment to one of the talocalcaneal ligaments.