A STUDENT PLT IN A C172 THOUGHT THAT ATC ISSUED A CLRNC TO TKOF. DURING TKOF A CONFLICT WITH A TWIN CESSNA OCCURRED.

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I MADE MY INITIAL CALL TO LINCOLN CLRNC FOR TOUCH AND GO TRAINING IN A 172 CESSNA. AS INSTRUCTED I PROCEEDED TO TXWY E FOR A RWY 17L DEP. AFTER PERFORMING MY RUN-UP; I CONTACTED LINCOLN TWR. I WAS INSTRUCTED BY TWR TO; 'HOLD SHORT ON TXWY E FOR RWY 17L.' I PROCEEDED TO THE HOLD SHORT MARK AND AIMED MY ACFT TO THE NW AS TO MORE EASILY SEE ANY TFC ON FINAL APCH FOR RWY 17L. AFTER A MIN OR SO LINCOLN TWR SAID; 'TAXI TO RWY 17L INTXN AND HOLD FOR IMMEDIATE DEP.' I THEN REPLIED STATING; 'ROGER' INSTEAD OF READING BACK MY INSTRUCTIONS TO THE TWR. THIS WAS WHEN THE MISUNDERSTANDING ON MY PART OCCURRED. I BEGAN MY TKOF ROLL WITHOUT HOLDING AND SHORTLY AFTER LIFTOFF I NOTICED A TWIN ENG CESSNA TAXIING ACROSS RWY 17L ON TXWY N. I BEGAN TO SECOND GUESS MYSELF AS TO HAVING DONE SOMETHING WRONG; BUT SINCE I DID NOT RECEIVE ANY SUCH INFO FROM LINCOLN TWR I ASSUMED I WAS OK AND PROCEEDED IN THE PATTERN. I PROCEEDED IN THE PATTERN FOR RWY 17L AND ON FINAL APCH I WAS TOLD TO MAKE A FULL STOP; I ASSUMED THIS WAS DUE TO SEVERAL ACFT WAITING TO TKOF ON RWY 17L; ALSO THE PATTERN WAS VERY FULL AND LINCOLN TWR WAS BUSY. UPON LNDG I TURNED ONTO TXWY K AND CONTACTED LINCOLN GND. I ASKED IF I COULD TAXI BACK TO TXWY E FOR RWY 17L. LINCOLN GND THEN INSTRUCTED ME TO TAXI TO THE E RAMP AND TO CALL LINCOLN TWR. IT WAS AT THIS TIME THAT I REALLY BEGAN TO QUESTION MYSELF AND REALIZED THAT I HAD MISUNDERSTOOD THE TWR'S INSTRUCTIONS TO 'HOLD FOR IMMEDIATE DEP.' I BELIEVE THAT IF I HAD INFORMED LINCOLN CLRNC AND LINCOLN TWR THAT I WAS A STUDENT PLT THAT THIS SIT MAY NOT HAVE OCCURRED. I ALSO BELIEVE THAT IF I HAD READ BACK TWR'S INSTRUCTIONS; INSTEAD OF SIMPLY SAYING; 'ROGER' THAT TWR MAY HAVE CAUGHT MY MISTAKE AND CORRECTED IT BEFORE THE MISTAKE OCCURRED.