Given number is $10800$

Prime factorisation of $10800$ is $2^4\times 3^3\times 5^2$

The total number of divisors $=\left(4+1\right)\left(3+1\right)\left(2+1\right)$

$=\left(5\right)\left(4\right)\left(3\right)$

$=60$

The number of odd divisors $=1\left(3+1\right)\left(2+1\right)$

$=1\left(4\right)\left(3\right)$

$=12$

The number of even divisors $=60-12$

$=48$

Here., $a=48, b=12$

$\Rightarrow 2\left(a\right)+3\left(b\right)=2\left(48\right)+3\left(12\right)$

$=96+36$

$\therefore 2a+3b=132$