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Ruby, 53 55 bytes

f=->(a,b){/^(2|too?|t0|two)$/i=~a&&/^(be{,2}|b3)$/i=~b} 

I'll be honest, this is my first attempt at trying to golf a problem.

Function call in the form of f.call(firstValue, secondValue)

0 is Truthy, nil is Falsy.

Test it Here

Ruby, 53 55 52 bytes

f=->(a,b){/^(2|t[wo]?o|t0)$/i=~a&&/^b(e?e?|3)$/i=~b} 

I'll be honest, this is my first attempt at trying to golf a problem.

Function call in the form of f.call(firstValue, secondValue)

0 is Truthy, nil is Falsy.

Test it Here

Ruby, 53 bytes

f=->(a,b){/^(2|too?|t0|two)$/i=~a&&/^be{,2}|b3$/i=~b} 

I'll be honest, this is my first attempt at trying to golf a problem.

Function call in the form of f.call(firstValue, secondValue)

0 is Truthy, nil is Falsy.

Test it Here

Ruby, 53 55 bytes

f=->(a,b){/^(2|too?|t0|two)$/i=~a&&/^(be{,2}|b3)$/i=~b} 

I'll be honest, this is my first attempt at trying to golf a problem.

Function call in the form of f.call(firstValue, secondValue)

0 is Truthy, nil is Falsy.

Test it Here

Ruby, 53 bytes

f=->(a,b){/^(2|too?|t0|two)$/i=~a&&/^be{,2}|b3$/i=~b} 

I'll be honest, this is my first attempt at trying to golf a problem.

Function call in the form of f.call(firstValue, secondValue)

0 is Truthy, nil is Falsy.

Ruby, 53 bytes

f=->(a,b){/^(2|too?|t0|two)$/i=~a&&/^be{,2}|b3$/i=~b} 

I'll be honest, this is my first attempt at trying to golf a problem.

Function call in the form of f.call(firstValue, secondValue)

0 is Truthy, nil is Falsy.

Test it Here