RWY INCURSION BY A C172 COMMERCIAL PLT AT TEB; NJ.

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I WAS CLRED BY TEB LCL ATC FROM THE RAMP ON TXWY G TO 'TAXI RWY 6 INTXN G.' I TAXIED ON TXWY G ACROSS RWY 6/24; AFTER LOOKING BOTH WAYS FOR OTHER ACFT; INTENDING TO TAXI ON TXWY G TO TXWY N TO THE DEP END OF RWY 6. INDEED; I TAXIED ACROSS RWY 6/24 ON TXWY G AND STOPPED AFTER REALIZING SOMETHING WAS WRONG. AT THIS POINT; ATC ASKED ME WHY I CROSSED RWY 6/24 AND ASKED ME TO MAKE A 180 DEG TURN AND HOLD AT RWY 6/24 ON TXWY G. I COMPLIED. IMMEDIATE INCIDENT WAS OVER. THEREAFTER; I HELD. ANOTHER ACFT (A C210) TAXIED TO TXWY G ON THE OTHER SIDE. WE BOTH HELD AT OUR RESPECTIVE POS. WITHIN A FEW MINS; C210 WAS CLRED FOR TKOF. HE DEPARTED WITHOUT INCIDENT. WITHIN A FEW MORE MINS; I WAS CLRED FOR TKOF. CONTRIBUTING FACTORS: FOR REASONS UNKNOWN TO ME; I MISUNDERSTOOD THE TAXI INSTRUCTIONS. CORRECTIVE ACTIONS AND FUTURE PREVENTION OF A SIMILAR INCIDENT: WITHIN 1 DAY; I CONSULTED WITH 2 VERY EXPERIENCED FLT INSTRUCTORS. I RELEARNED THAT ALL RWYS MAY BE CROSSED EXCEPT FOR THE ONE WHICH ONE HAS BEEN CLRED TO; UNLESS OTHERWISE INSTRUCTED. FURTHER; WE DISCUSSED TAXI INSTRUCTIONS IN GREAT DETAIL (SORT OF A REFRESHER COURSE). THIS INCIDENT MAY HAVE BEEN AVOIDED HAD I BEEN THINKING MORE CLRLY AND IF ATC (AS A COURTESY) INSTRUCTED ME TO HOLD SHORT (NOT CROSS) RWY 6/24.