let

p = the number of pizzas

h = the number of hamburgers

t = the number of tacos

he bought twice as many hamburgers as pizzas

h = 2p

and six more tacos than hamburgers

t = h + 6

he bought 16 items altogether

p + h + t = 16

by solving the system of equations

h = 2p

t = h + 6

p + h + t = 16

we find

h = 4 hamburgers

p = 2 pizzas

t = 10 tacos

click here to see the step by step solution of the system of eqautions