Step 1: Read the question. We must find which form of carbon conducts both heat and electricity well.
Step 2: Look at graphite's structure. In graphite each carbon atom bonds to only three other carbons. These atoms form flat hexagon-shaped layers.
Step 3: Find the free electron. Carbon has four outer electrons but graphite uses only three for bonding. The fourth electron is left free to move.
Step 4: Connect free electrons to conduction. Moving electrons carry electric current. These free electrons drift through the layers, so graphite conducts electricity and also carries heat well.
Step 5: Compare with diamond. In diamond all four electrons are tied up in bonds. No electron is free, so diamond cannot conduct.
Step 6: Pick the answer. The conducting form of carbon is graphite. \[ \boxed{\text{Graphite}} \]